(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 13.1' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 298938, 7274] NotebookOptionsPosition[ 287319, 7003] NotebookOutlinePosition[ 290487, 7087] CellTagsIndexPosition[ 290408, 7082] WindowTitle->GenerateTiling | Example Notebook WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell[TextData[{ "Basic Examples", "\[NonBreakingSpace]", Cell["(4)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellTags->"DefaultContent", CellID->279727361], Cell["Generate a uniform tiling pattern of all 0s:", "Text", TaggingRules->{}, CellChangeTimes->{{3.8648206882118397`*^9, 3.864820697189178*^9}, 3.867855480617216*^9}, CellID->848888257], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{ RowBox[{"{", " ", RowBox[{"{", RowBox[{"{", "0", "}"}], "}"}], " ", "}"}], ",", RowBox[{"{", "}"}], ",", "4"}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648203094841022`*^9, 3.864820387914887*^9}, { 3.864820514906114*^9, 3.864820515066373*^9}, {3.8648206770653677`*^9, 3.864820714622531*^9}, {3.864820798897574*^9, 3.864820803438334*^9}}, CellLabel->"In[1]:=", CellID->714828949], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "0", ",", "0", ",", "0"}], "}"}]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864820311803793*^9, 3.864820388638832*^9}, { 3.864820419323291*^9, 3.864820446961966*^9}, {3.864820505134264*^9, 3.864820515626856*^9}, {3.864820664577106*^9, 3.8648206796336603`*^9}, 3.864820715666506*^9, 3.864820804024629*^9, 3.864822729217868*^9, 3.864825943468192*^9}, CellLabel->"Out[1]=", CellID->699937031] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->2016696111], Cell["\<\ Generate uniform tiling patterns for the first few positive integers:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.8648206882118397`*^9, 3.864820697189178*^9}, { 3.864820728702218*^9, 3.864820783475721*^9}}, CellID->356300994], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ RowBox[{ RowBox[{"MatrixForm", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{ RowBox[{"{", " ", RowBox[{"{", RowBox[{"{", "#", "}"}], "}"}], " ", "}"}], ",", RowBox[{"{", "}"}], ",", "4"}], "]"}]}], "&"}], "/@", RowBox[{"Range", "[", "5", "]"}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648203094841022`*^9, 3.864820387914887*^9}, { 3.864820514906114*^9, 3.864820515066373*^9}, {3.8648206770653677`*^9, 3.8648207727188053`*^9}, {3.864820805368063*^9, 3.864820812854134*^9}}, CellLabel->"In[2]:=", CellID->416008876], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"1", "1", "1", "1"}, {"1", "1", "1", "1"}, {"1", "1", "1", "1"}, {"1", "1", "1", "1"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"2", "2", "2", "2"}, {"2", "2", "2", "2"}, {"2", "2", "2", "2"}, {"2", "2", "2", "2"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"3", "3", "3", "3"}, {"3", "3", "3", "3"}, {"3", "3", "3", "3"}, {"3", "3", "3", "3"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"4", "4", "4", "4"}, {"4", "4", "4", "4"}, {"4", "4", "4", "4"}, {"4", "4", "4", "4"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]], ",", TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"5", "5", "5", "5"}, {"5", "5", "5", "5"}, {"5", "5", "5", "5"}, {"5", "5", "5", "5"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864820311803793*^9, 3.864820388638832*^9}, { 3.864820419323291*^9, 3.864820446961966*^9}, {3.864820505134264*^9, 3.864820515626856*^9}, {3.864820664577106*^9, 3.8648206796336603`*^9}, { 3.864820715666506*^9, 3.8648207731137*^9}, {3.86482080717981*^9, 3.864820813062292*^9}, 3.864822729252508*^9, 3.8648259435030994`*^9}, CellLabel->"Out[2]=", CellID->852863177] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->14107562], Cell["Generate a tiling pattern from a set of three templates:", "Text", TaggingRules->{}, CellChangeTimes->{{3.856263865682458*^9, 3.8562638758087006`*^9}, { 3.864815612366379*^9, 3.864815625812007*^9}}, CellTags->"DefaultContent", CellID->512168029], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"MatrixForm", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}], ",", "5"}], "]"}]}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8560150785894165`*^9, 3.856015080828805*^9}, { 3.8560158071604033`*^9, 3.856015842990318*^9}, {3.856259746272606*^9, 3.856259746419601*^9}, {3.856263766374446*^9, 3.8562637897249317`*^9}, { 3.864808049784049*^9, 3.864808068260517*^9}, 3.864808244719048*^9, { 3.864813371762513*^9, 3.864813378594119*^9}, {3.864820829006311*^9, 3.864820853278866*^9}}, CellLabel->"In[1]:=", CellID->359746122], Cell[BoxData[ TagBox[ RowBox[{"(", "\[NoBreak]", GridBox[{ {"0", "1", "1", "0", "1"}, {"1", "0", "1", "1", "0"}, {"1", "1", "0", "1", "1"}, {"0", "1", "1", "0", "1"}, {"1", "0", "1", "1", "0"} }, GridBoxAlignment->{"Columns" -> {{Center}}, "Rows" -> {{Baseline}}}, GridBoxSpacings->{"Columns" -> { Offset[0.27999999999999997`], { Offset[0.7]}, Offset[0.27999999999999997`]}, "Rows" -> { Offset[0.2], { Offset[0.4]}, Offset[0.2]}}], "\[NoBreak]", ")"}], Function[BoxForm`e$, MatrixForm[BoxForm`e$]]]], "Output", TaggingRules->{}, CellChangeTimes->{{3.856015814721883*^9, 3.856015843867592*^9}, 3.8562596205243416`*^9, 3.856259747453347*^9, 3.8562598301476398`*^9, { 3.856263831044533*^9, 3.8562638467332487`*^9}, {3.856272924239959*^9, 3.856272941100709*^9}, 3.8562729993001304`*^9, {3.8572256423103704`*^9, 3.857225653247716*^9}, 3.8648075983595343`*^9, {3.864807838037065*^9, 3.864807846659383*^9}, 3.864808071359352*^9, 3.8648102582066517`*^9, 3.864810312740494*^9, {3.8648103444306498`*^9, 3.864810371463141*^9}, 3.8648104234467297`*^9, {3.8648133719845257`*^9, 3.86481337878722*^9}, 3.864820541199737*^9, 3.864820786216488*^9, {3.864820830688181*^9, 3.864820853485797*^9}, 3.8648227292932377`*^9, 3.864825943535113*^9}, CellLabel->"Out[1]//MatrixForm=", CellID->918374088] }, Open ]], Cell[TextData[{ "Plot the tiling pattern using ", Cell[BoxData[ TagBox[ ButtonBox[ StyleBox["ArrayPlot", "SymbolsRefLink", ShowStringCharacters->True, FontFamily->"Source Sans Pro"], BaseStyle->Dynamic[ FEPrivate`If[ CurrentValue["MouseOver"], { "Link", FontColor -> RGBColor[0.8549, 0.39608, 0.1451]}, {"Link"}]], ButtonData->"paclet:ref/ArrayPlot", ContentPadding->False], MouseAppearanceTag["LinkHand"]]], "InlineFormula", FontFamily->"Source Sans Pro"], ", and use the resource function ", ButtonBox["TilingPatternPlot", BaseStyle->"Hyperlink", ButtonData->{ URL["https://resources.wolframcloud.com/FunctionRepository/resources/\ TilingPatternPlot"], None}, ButtonNote-> "https://resources.wolframcloud.com/FunctionRepository/resources/\ TilingPatternPlot"], " to show the templates used:" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.856263909271064*^9, 3.8562639145039682`*^9}, { 3.864809081977664*^9, 3.864809088640244*^9}, {3.864815651337315*^9, 3.8648156560661707`*^9}, {3.8692350764431057`*^9, 3.86923511536862*^9}, 3.869235246049061*^9}, CellID->868970757], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"tiles", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"tiling", "=", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", "20"}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"tiling", ",", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "10"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{ RowBox[{ RowBox[{"ResourceFunction", "[", "\"\\"", "]"}], "[", RowBox[{"tiles", ",", " ", RowBox[{"ImageSize", "->", " ", "50"}]}], "]"}], ",", RowBox[{"Spacer", "[", "20", "]"}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "Input", TaggingRules->{}, CellChangeTimes->{{3.864808240435195*^9, 3.8648083123862877`*^9}, { 3.864826033794957*^9, 3.864826139342103*^9}, {3.8648261728307295`*^9, 3.8648262077417784`*^9}, {3.8648262455959144`*^9, 3.864826245702347*^9}}, CellLabel->"In[14]:=", CellID->775865682], Cell[BoxData[ TemplateBox[{ GraphicsBox[ RasterBox[CompressedData[" 1:eJxTTMoPSmJiYGAQgWIGRkyERQirwlG91NcLAFkRAlc= "], {{0, 0}, Offset[{200, 200}, {0, 0}]}, {0, 1}], ImageSize -> {200, 200}, PlotRange -> {{0, 200}, {0, 200}}, PlotRangeClipping -> True, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TemplateBox[{ TemplateBox[{20}, "Spacer1"], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {2, 2}, 1., {1, {{0, 1, 2}, {{1}, {2}}}, {0., 0.}}], {{0, 0}, {2, 2}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, CoordinatesToolOptions -> Automatic, DisplayFunction :> $DisplayFunction, Epilog -> {}, FormatType :> TraditionalForm, Frame -> False, FrameLabel -> {None, None}, FrameStyle -> {}, FrameTicks -> {{None, None}, {None, None}}, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> 50, ImageSizeRaw -> Automatic, LabelStyle -> {}, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}, PlotLabel -> None, PlotRangeClipping -> False, PlotRangePadding -> 0, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {2, 2}, 1., { 1, {{0, 2, 3}, {{1}, {2}, {1}}}, {0., 0., 0.}}], {{0, 0}, {2, 2}}, { 0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, CoordinatesToolOptions -> Automatic, DisplayFunction :> $DisplayFunction, Epilog -> {}, FormatType :> TraditionalForm, Frame -> False, FrameLabel -> {None, None}, FrameStyle -> {}, FrameTicks -> {{None, None}, {None, None}}, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> 50, ImageSizeRaw -> Automatic, LabelStyle -> {}, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}, PlotLabel -> None, PlotRangeClipping -> False, PlotRangePadding -> 0, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {2, 2}, 1., { 1, {{0, 1, 3}, {{2}, {1}, {2}}}, {0., 0., 0.}}], {{0, 0}, {2, 2}}, { 0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, AlignmentPoint -> Center, AspectRatio -> Automatic, Axes -> False, AxesLabel -> None, AxesOrigin -> Automatic, AxesStyle -> {}, Background -> None, BaselinePosition -> Automatic, BaseStyle -> {}, ColorOutput -> Automatic, ContentSelectable -> Automatic, CoordinatesToolOptions -> Automatic, DisplayFunction :> $DisplayFunction, Epilog -> {}, FormatType :> TraditionalForm, Frame -> False, FrameLabel -> {None, None}, FrameStyle -> {}, FrameTicks -> {{None, None}, {None, None}}, FrameTicksStyle -> {}, GridLines -> None, GridLinesStyle -> {}, ImageMargins -> 0., ImagePadding -> All, ImageSize -> 50, ImageSizeRaw -> Automatic, LabelStyle -> {}, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}, PlotLabel -> None, PlotRangeClipping -> False, PlotRangePadding -> 0, PlotRegion -> Automatic, PreserveImageOptions -> Automatic, Prolog -> {}, RotateLabel -> True, Ticks -> Automatic, TicksStyle -> {}]}, "RowWithSeparator"]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864808268142983*^9, 3.864808302264461*^9}, 3.8648104260642014`*^9, 3.8648205491883307`*^9, 3.864820861498612*^9, 3.864822729536189*^9, 3.864825943886134*^9, 3.864826142947654*^9, { 3.8648261805898137`*^9, 3.8648262084876957`*^9}, 3.864826246494111*^9}, CellLabel->"Out[16]=", CellID->89588579] }, Open ]], Cell["\<\ Change the dimensions of the tiling pattern and break up the result into \ generating tiles:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.856263909271064*^9, 3.8562639145039682`*^9}, { 3.864809081977664*^9, 3.864809088640244*^9}, {3.864815651337315*^9, 3.8648156823469133`*^9}, {3.8648263543578606`*^9, 3.864826381711442*^9}}, CellID->667907404], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"tiles", "=", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "0"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"0", ",", "1"}], "}"}]}], "}"}]}], "}"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"tiling", "=", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"10", ",", "20"}], "}"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"tiling", ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "10"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ImageSize", "\[Rule]", "50"}], ",", RowBox[{"Mesh", "->", "True"}]}], "]"}], "&"}], "/@", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{"tiling", ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "]"}], ",", "1"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Spacer", "[", "5", "]"}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648090522527514`*^9, 3.864809054061903*^9}, { 3.864826288499564*^9, 3.8648263194985533`*^9}, 3.8648263496961956`*^9}, CellLabel->"In[20]:=", CellID->9502071], Cell[BoxData[ TemplateBox[{ GraphicsBox[ RasterBox[{{1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0}, { 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0}, {0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0}, {0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1}, {1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0}}, {{0, 0}, Offset[{200, 100}, {0, 0}]}, {0, 1}], ImageSize -> {200, 100}, PlotRange -> {{0, 200}, {0, 100}}, PlotRangeClipping -> True, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TemplateBox[{ TemplateBox[{5}, "Spacer1"], GraphicsBox[{ RasterBox[{{0, 1}, {1, 0}}, {{0, 0}, {2, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 0}, {0, 1}}, {{0, 0}, {2, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 0}, {0, 0}}, {{0, 0}, {2, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}, "RowWithSeparator"]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{ 3.8648090550807734`*^9, 3.864810428218458*^9, 3.86482272976794*^9, 3.8648259441046553`*^9, {3.8648263459720745`*^9, 3.8648263504040194`*^9}}, CellLabel->"Out[22]=", CellID->610914188] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->14107563], Cell["Plot a four-color periodic tiling pattern:", "Text", TaggingRules->{}, CellChangeTimes->{{3.864816052839595*^9, 3.864816085073738*^9}, { 3.867855505633293*^9, 3.867855508064345*^9}}, CellID->295611003], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"tiling", "=", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{"RotateRight", "[", RowBox[{ RowBox[{"Range", "[", RowBox[{"0", ",", "3"}], "]"}], ",", "#"}], "]"}], ",", "2"}], "]"}], "&"}], "/@", RowBox[{"Range", "[", "4", "]"}]}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"20", ",", "20"}], "}"}]}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"colRules", "=", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "->", "#1"}], "&"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Blend", "[", RowBox[{"{", RowBox[{"Yellow", ",", "Orange"}], "}"}], "]"}], ",", RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Green", ",", "Cyan"}], "}"}], ",", ".5"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Lighter", "[", RowBox[{"Blue", ",", ".5"}], "]"}], ",", RowBox[{"Lighter", "[", RowBox[{ RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Magenta", ",", "Red"}], "}"}], ",", ".25"}], "]"}], ",", "0.4"}], "]"}]}], "}"}]}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"tiling", ",", RowBox[{"ColorRules", "->", "colRules"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "True"}], ",", RowBox[{"MeshStyle", "\[Rule]", "Black"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Row", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ColorRules", "\[Rule]", "colRules"}], ",", "\[IndentingNewLine]", RowBox[{"ImageSize", "\[Rule]", "50"}], ",", RowBox[{"Mesh", "->", "True"}], ",", RowBox[{"MeshStyle", "\[Rule]", "Black"}]}], "\[IndentingNewLine]", "]"}], "&"}], "/@", RowBox[{"Union", "[", RowBox[{"Flatten", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{"tiling", ",", RowBox[{"{", RowBox[{"2", ",", "2"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "]"}], ",", "1"}], "]"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"Spacer", "[", "5", "]"}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864815777225604*^9, 3.864815843000779*^9}, { 3.864815895279333*^9, 3.864815934306151*^9}, {3.864815970965423*^9, 3.864815999271456*^9}, {3.864816110710586*^9, 3.8648161172236443`*^9}, { 3.86482089202841*^9, 3.8648208947862883`*^9}}, CellLabel->"In[1]:=", CellID->320857703], Cell[BoxData[ TemplateBox[{ GraphicsBox[{ RasterBox[CompressedData[" 1:eJztzsEJg0AABdEFW7CB1GAB24MlBHK2Hu3MW46BXCwhGENA8fjBOcyHZRcW HnO7D/2jKaW0v7O+tz3r/l7+9zSum2v33fvw/6rldMvB07/Wp/XoZ31aj37W p/XoZ31aj37Wp/XoZ31aj37Wp/XoZ31aj37Wp/XoZ31aj37Wp/XoZ31aj37W p/XoZ31aj37Wp/XoZ31aj37Wp/XoZ31aj37Wp/Xop/wPaXxffg== "], {{0, 0}, {20, 20}}, {0, 1}], {{Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 20}, {20, 20}}, {{0, 19}, {20, 19}}, {{0, 18}, {20, 18}}, {{0, 17}, {20, 17}}, {{0, 16}, {20, 16}}, {{0, 15}, {20, 15}}, {{0, 14}, {20, 14}}, {{0, 13}, {20, 13}}, {{0, 12}, {20, 12}}, {{0, 11}, {20, 11}}, {{0, 10}, {20, 10}}, {{0, 9}, {20, 9}}, {{ 0, 8}, {20, 8}}, {{0, 7}, {20, 7}}, {{0, 6}, {20, 6}}, {{0, 5}, {20, 5}}, {{0, 4}, {20, 4}}, {{0, 3}, {20, 3}}, {{0, 2}, {20, 2}}, {{0, 1}, {20, 1}}, {{0, 0}, {20, 0}}}]}, {Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 0}, {0, 20}}, {{1, 0}, {1, 20}}, {{2, 0}, {2, 20}}, {{3, 0}, {3, 20}}, {{4, 0}, {4, 20}}, {{5, 0}, {5, 20}}, {{6, 0}, {6, 20}}, {{7, 0}, {7, 20}}, {{8, 0}, {8, 20}}, {{9, 0}, {9, 20}}, {{10, 0}, {10, 20}}, {{11, 0}, {11, 20}}, {{12, 0}, {12, 20}}, {{13, 0}, { 13, 20}}, {{14, 0}, {14, 20}}, {{15, 0}, {15, 20}}, {{16, 0}, {16, 20}}, {{17, 0}, {17, 20}}, {{18, 0}, {18, 20}}, {{19, 0}, {19, 20}}, {{20, 0}, {20, 20}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TemplateBox[{ TemplateBox[{5}, "Spacer1"], GraphicsBox[{ RasterBox[{{{0.5, 0.5, 1.}, {1., 0.4, 0.85}}, {{1., 0.75, 0.}, {0., 1., 0.5}}}, {{0, 0}, {2, 2}}, {0, 1}], {{Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{{1., 0.4, 0.85}, {1., 0.75, 0.}}, {{0., 1., 0.5}, {0.5, 0.5, 1.}}}, {{0, 0}, {2, 2}}, {0, 1}], {{Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{{1., 0.75, 0.}, {0., 1., 0.5}}, {{0.5, 0.5, 1.}, {1., 0.4, 0.85}}}, {{0, 0}, {2, 2}}, {0, 1}], {{Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{{0., 1., 0.5}, {0.5, 0.5, 1.}}, {{1., 0.4, 0.85}, {1., 0.75, 0.}}}, {{0, 0}, {2, 2}}, {0, 1}], {{Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 2}, {2, 2}}, {{0, 1}, {2, 1}}, {{0, 0}, {2, 0}}}]}, { Antialiasing -> False, GrayLevel[0], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}, "RowWithSeparator"]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{{3.8648157925413723`*^9, 3.864815812074279*^9}, { 3.864815905731007*^9, 3.86481593490234*^9}, 3.8648159833205633`*^9, 3.864816118402052*^9, 3.864822730087112*^9, 3.8648259444882526`*^9}, CellLabel->"Out[1]=", CellID->844591674] }, Open ]], Cell["Plot all four translates of this tiling pattern:", "Text", TaggingRules->{}, CellChangeTimes->{{3.864816175538929*^9, 3.864816188425375*^9}}, CellID->727395058], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"tilings", "=", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{"RotateRight", "[", RowBox[{ RowBox[{"Range", "[", RowBox[{"0", ",", "3"}], "]"}], ",", "#"}], "]"}], ",", "2"}], "]"}], "&"}], "/@", RowBox[{"Range", "[", "4", "]"}]}], ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"12", ",", "12"}], "}"}], ",", "All"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"colRules", "=", RowBox[{"MapIndexed", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"#2", "[", RowBox[{"[", "1", "]"}], "]"}], "-", "1"}], ")"}], "->", "#1"}], "&"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Blend", "[", RowBox[{"{", RowBox[{"Yellow", ",", "Orange"}], "}"}], "]"}], ",", RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Green", ",", "Cyan"}], "}"}], ",", ".5"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Lighter", "[", RowBox[{"Blue", ",", ".5"}], "]"}], ",", RowBox[{"Lighter", "[", RowBox[{ RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Magenta", ",", "Red"}], "}"}], ",", ".25"}], "]"}], ",", "0.4"}], "]"}]}], "}"}]}], "]"}]}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ColorRules", "->", "colRules"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "True"}], ",", RowBox[{"MeshStyle", "\[Rule]", "Black"}]}], "}"}]}], "]"}], "&"}], "/@", "tilings"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864816097885069*^9, 3.864816163555197*^9}}, CellLabel->"In[2]:=", CellID->130252101], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[{RasterBox[CompressedData[" 1:eJxTTMoPSmVmYGDggWIQGxV8sIfQD3DQH+D0rJkgcNPeGAxeo8m/sMcwekib P9jcM9jMH2zuGWzmDzb3DDbzB5t7Bpv5g809g838weaewWb+YHPPYDN/sLln sJk/2Nwz2MwfbO4ZbOYPNvcMHvMBbmhMcg== "], {{0, 0}, {12, 12}}, {0, 1}], { {GrayLevel[0], StyleBox[ LineBox[{{{0, 12}, {12, 12}}, {{0, 11}, {12, 11}}, {{0, 10}, {12, 10}}, {{0, 9}, {12, 9}}, {{0, 8}, {12, 8}}, {{0, 7}, {12, 7}}, {{0, 6}, {12, 6}}, {{0, 5}, {12, 5}}, {{0, 4}, {12, 4}}, {{0, 3}, {12, 3}}, {{0, 2}, {12, 2}}, {{0, 1}, {12, 1}}, {{0, 0}, {12, 0}}}], Antialiasing->False]}, {GrayLevel[0], StyleBox[ LineBox[{{{0, 0}, {0, 12}}, {{1, 0}, {1, 12}}, {{2, 0}, {2, 12}}, {{3, 0}, {3, 12}}, {{4, 0}, {4, 12}}, {{5, 0}, {5, 12}}, {{6, 0}, {6, 12}}, {{7, 0}, {7, 12}}, {{8, 0}, {8, 12}}, {{9, 0}, {9, 12}}, {{10, 0}, {10, 12}}, {{11, 0}, {11, 12}}, {{12, 0}, {12, 12}}}], Antialiasing->False]}}}, Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], ",", GraphicsBox[{RasterBox[CompressedData[" 1:eJzVzr0JgDAQgNGArUs4gwNkB0cQrJ1HN7OzFGwygsS/QrR/HoQLHDy+qu2b rgghlOfL/2NSPPYSw+tc9/ljp3uPQ54p1vusj/tffa1H87Uezdd6NF/r0Xyt R/O1Hs3XejRf69F8rUfztR7N13ocfwNUmExy "], {{0, 0}, {12, 12}}, {0, 1}], { {GrayLevel[0], StyleBox[ LineBox[{{{0, 12}, {12, 12}}, {{0, 11}, {12, 11}}, {{0, 10}, {12, 10}}, {{0, 9}, {12, 9}}, {{0, 8}, {12, 8}}, {{0, 7}, {12, 7}}, {{0, 6}, {12, 6}}, {{0, 5}, {12, 5}}, {{0, 4}, {12, 4}}, {{0, 3}, {12, 3}}, {{0, 2}, {12, 2}}, {{0, 1}, {12, 1}}, {{0, 0}, {12, 0}}}], Antialiasing->False]}, {GrayLevel[0], StyleBox[ LineBox[{{{0, 0}, {0, 12}}, {{1, 0}, {1, 12}}, {{2, 0}, {2, 12}}, {{3, 0}, {3, 12}}, {{4, 0}, {4, 12}}, {{5, 0}, {5, 12}}, {{6, 0}, {6, 12}}, {{7, 0}, {7, 12}}, {{8, 0}, {8, 12}}, {{9, 0}, {9, 12}}, {{10, 0}, {10, 12}}, {{11, 0}, {11, 12}}, {{12, 0}, {12, 12}}}], Antialiasing->False]}}}, Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], ",", GraphicsBox[{RasterBox[CompressedData[" 1:eJzVzrEJgDAQQNGArUs4gwNkB0cQrJ1HN7OzFGwygsSolfbPg3Ahgcdv+rEb qhBCfZ18L5PiPOVZYnvOHu/3srcYXuf+Xz92eva/fa1H87Uezdd6NF/r0Xyt R/O1Hs3XejRf69F8rUfztR7N13oc/wBuaExy "], {{0, 0}, {12, 12}}, {0, 1}], { {GrayLevel[0], StyleBox[ LineBox[{{{0, 12}, {12, 12}}, {{0, 11}, {12, 11}}, {{0, 10}, {12, 10}}, {{0, 9}, {12, 9}}, {{0, 8}, {12, 8}}, {{0, 7}, {12, 7}}, {{0, 6}, {12, 6}}, {{0, 5}, {12, 5}}, {{0, 4}, {12, 4}}, {{0, 3}, {12, 3}}, {{0, 2}, {12, 2}}, {{0, 1}, {12, 1}}, {{0, 0}, {12, 0}}}], Antialiasing->False]}, {GrayLevel[0], StyleBox[ LineBox[{{{0, 0}, {0, 12}}, {{1, 0}, {1, 12}}, {{2, 0}, {2, 12}}, {{3, 0}, {3, 12}}, {{4, 0}, {4, 12}}, {{5, 0}, {5, 12}}, {{6, 0}, {6, 12}}, {{7, 0}, {7, 12}}, {{8, 0}, {8, 12}}, {{9, 0}, {9, 12}}, {{10, 0}, {10, 12}}, {{11, 0}, {11, 12}}, {{12, 0}, {12, 12}}}], Antialiasing->False]}}}, Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], ",", GraphicsBox[{RasterBox[CompressedData[" 1:eJzVzrEJgDAARcGArUs4gwNkB0cQrJ1HN7OzFGwygkRFMDjA+SEkEDhe04/d UIUQ6vvk97U1vu/03POUt8T23F78bzF8LhXe332tR/O1Hs3XejRf69F8rUfz tR7N13o0X+vRfK1H87Uezdd6HP8AVJhMcg== "], {{0, 0}, {12, 12}}, {0, 1}], { {GrayLevel[0], StyleBox[ LineBox[{{{0, 12}, {12, 12}}, {{0, 11}, {12, 11}}, {{0, 10}, {12, 10}}, {{0, 9}, {12, 9}}, {{0, 8}, {12, 8}}, {{0, 7}, {12, 7}}, {{0, 6}, {12, 6}}, {{0, 5}, {12, 5}}, {{0, 4}, {12, 4}}, {{0, 3}, {12, 3}}, {{0, 2}, {12, 2}}, {{0, 1}, {12, 1}}, {{0, 0}, {12, 0}}}], Antialiasing->False]}, {GrayLevel[0], StyleBox[ LineBox[{{{0, 0}, {0, 12}}, {{1, 0}, {1, 12}}, {{2, 0}, {2, 12}}, {{3, 0}, {3, 12}}, {{4, 0}, {4, 12}}, {{5, 0}, {5, 12}}, {{6, 0}, {6, 12}}, {{7, 0}, {7, 12}}, {{8, 0}, {8, 12}}, {{9, 0}, {9, 12}}, {{10, 0}, {10, 12}}, {{11, 0}, {11, 12}}, {{12, 0}, {12, 12}}}], Antialiasing->False]}}}, Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864816125152082*^9, 3.864816152306571*^9}, 3.8648227334756536`*^9, 3.8648259477333755`*^9}, CellLabel->"Out[2]=", CellID->334403499] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[TextData[{ "Scope", "\[NonBreakingSpace]", Cell["(2)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellTags->"DefaultContent", CellID->513869560], Cell["\<\ Generate a tiling pattern from a complicated set of templates:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.856264042708762*^9, 3.8562640721219115`*^9}, { 3.864816480960218*^9, 3.864816484631187*^9}}, CellTags->"DefaultContent", CellID->907666835], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"13", ",", "2", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["3784", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{0, 1, 1}, {1, 1, 1}}, {{1, 0, 1}, {1, 1, 1}}, {{1, 1, 0}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}}, {{0, 1, 0}, {0, 0, 0}}, {{0, 0, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 1, 0}}, {{0, 0, 0}, {1, 0, 0}}, {{1, 0, 1}, {0, 0, 0}}, {{1, 1, 1}, {0, 1, 0}}, {{0, 0, 1}, {0, 1, 1}}, {{0, 1, 0}, {1, 1, 0}}, {{1, 0, 0}, {1, 0, 1}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", "30"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "10"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Grid", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{"Append", "[", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ImageSize", "\[Rule]", "50"}], ",", RowBox[{"Mesh", "->", "True"}]}], "]"}], "&"}], "/@", "tiles"}], ",", "\"\<\>\""}], "]"}], ",", "7"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Spacings", "->", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864816399215171*^9, 3.864816461758212*^9}, 3.864818444132992*^9}, CellLabel->"In[1]:=", CellID->251372788], Cell[BoxData[ TemplateBox[{ GraphicsBox[ RasterBox[CompressedData[" 1:eJxTTMoPSmJiYGCQg2JG/IgRP8ILGPBBQmBAHEXAWYMzrAanq2jnKIpcRUFg 0S5dAQDtGgOn "], {{0, 0}, Offset[{300, 300}, {0, 0}]}, {0, 1}], ImageSize -> {300, 300}, PlotRange -> {{0, 300}, {0, 300}}, PlotRangeClipping -> True, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TagBox[ GridBox[{{ GraphicsBox[{ RasterBox[{{0, 0, 0}, {1, 0, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 0, 0}, {0, 1, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 0, 0}, {0, 0, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 1, 0}, {0, 0, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 1, 1}, {1, 0, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 1, 0}, {1, 1, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 0, 1}, {1, 1, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}, { GraphicsBox[{ RasterBox[{{0, 1, 1}, {1, 1, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 1, 1}, {0, 1, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 0, 1}, {0, 0, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{1, 0, 0}, {1, 1, 0}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 0, 1}, {1, 0, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[{{0, 1, 0}, {0, 1, 1}}, {{0, 0}, {3, 2}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{0, 0}, {3, 0}}}]}, { Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 2}}, {{1, 0}, {1, 2}}, {{2, 0}, {2, 2}}, {{3, 0}, {3, 2}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], "\"\""}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}], "Grid"]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{3.864816419549202*^9, 3.864816463079938*^9, 3.8648227347188272`*^9, 3.864825948870446*^9}, CellLabel->"Out[1]=", CellID->53467947] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->14107564], Cell[TextData[{ "Control the offset of a periodic tiling pattern by setting a ", Cell[BoxData[ StyleBox["seed", "TI"]], "InlineFormula", FontFamily->"Source Sans Pro"], " value:" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.8562701398090844`*^9, 3.856270191213179*^9}, { 3.864816918999284*^9, 3.864816940546399*^9}}, CellID->16002939], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}]}], "}"}], "&"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RotateRight", "[", RowBox[{ RowBox[{"Range", "[", "3", "]"}], ",", "#"}], "]"}], "&"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", "2"}], "]"}]}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", RowBox[{"{", "#", "}"}], "}"}], ",", "5"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Frame", "->", "None"}], ",", RowBox[{"ColorRules", "\[Rule]", RowBox[{"{", "\[IndentingNewLine]", RowBox[{ RowBox[{"1", "->", RowBox[{"Lighter", "[", RowBox[{ RowBox[{"Blend", "[", RowBox[{"{", RowBox[{"Red", ",", "Orange"}], "}"}], "]"}], ",", ".25"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"2", "->", RowBox[{"Darker", "[", RowBox[{ RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Green", ",", "Yellow"}], "}"}], ",", ".6"}], "]"}], ",", ".1"}], "]"}]}], ",", "\[IndentingNewLine]", RowBox[{"3", "->", RowBox[{"Lighter", "[", RowBox[{ RowBox[{"Blend", "[", RowBox[{ RowBox[{"{", RowBox[{"Blue", ",", "Green"}], "}"}], ",", ".2"}], "]"}], ",", ".35"}], "]"}]}]}], "}"}]}]}], "\[IndentingNewLine]", "]"}], "&"}], "/@", RowBox[{"Range", "[", "3", "]"}]}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864816780283062*^9, 3.864816894939362*^9}, { 3.864816950333241*^9, 3.864817160768463*^9}}, CellLabel->"In[1]:=", CellID->879643092], Cell[BoxData[ RowBox[{"{", RowBox[{ GraphicsBox[RasterBox[CompressedData[" 1:eJxTTMoPSmVmYGBghWIQGwI+2EPoO1D6gr3HwyqRde4P7c+eAYE39jCVaWBw zX6HXOvrwB337K8vLrDluv7aftScUXOQzQEAWKHOkw== "], {{0, 0}, {5, 5}}, {0, 1}], Frame->None, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], ",", GraphicsBox[RasterBox[CompressedData[" 1:eJxTTMoPSmVmYGBghWIQ2+Nhlcg694f2Z8+AwBt7BihIA4Nr9jvkWl8H7rhn f31xgS3X9ddQ+Q9Q+g6UvmA/as6oOcjmAAAtWNT6 "], {{0, 0}, {5, 5}}, {0, 1}], Frame->None, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], ",", GraphicsBox[RasterBox[CompressedData[" 1:eJxTTMoPSmVmYGBghWIQOw0MrtnvkGt9Hbjjnv31xQW2XNdf2zOAwQcofQdK X7D3eFglss79of3ZMyDwBio+as6oOajmAAAYmtdR "], {{0, 0}, {5, 5}}, {0, 1}], Frame->None, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{{3.8648170917060747`*^9, 3.864817161422968*^9}, 3.86482273489611*^9, 3.8648259490919495`*^9}, CellLabel->"Out[1]=", CellID->323466370] }, Open ]], Cell[TextData[{ "A tiling pattern around an ", Cell[BoxData[ RowBox[{"{", RowBox[{"{", RowBox[{ StyleBox["n", "TI"], ",", StyleBox["n", "TI"]}], "}"}], "}"}]], "InlineFormula", FontFamily->"Source Sans Pro"], " initial condition is not possible for this set of tiles:" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.8562701162152443`*^9, 3.856270119162801*^9}, { 3.856270198883379*^9, 3.856270224899692*^9}, {3.856270281404917*^9, 3.856270286315322*^9}, {3.8648172132578783`*^9, 3.864817214502734*^9}, { 3.864819807029203*^9, 3.864819814492545*^9}, {3.8678555231757936`*^9, 3.8678555326376266`*^9}, 3.8678577325477343`*^9}, CellID->46993719], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", RowBox[{"Map", "[", RowBox[{ RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "1", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"#", "[", RowBox[{"[", "2", "]"}], "]"}], ",", RowBox[{"#", "[", RowBox[{"[", "3", "]"}], "]"}]}], "}"}]}], "}"}], "&"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"RotateRight", "[", RowBox[{ RowBox[{"Range", "[", "3", "]"}], ",", "#"}], "]"}], "&"}], "/@", RowBox[{"Range", "[", RowBox[{"0", ",", "2"}], "]"}]}]}], "]"}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", RowBox[{"{", RowBox[{"#", ",", "#"}], "}"}], "}"}], ",", "5"}], "]"}], "&"}], "/@", RowBox[{"Range", "[", "3", "]"}]}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864817194379916*^9, 3.864817199540498*^9}}, CellLabel->"In[2]:=", CellID->421932251], Cell[BoxData[ RowBox[{"{", RowBox[{ InterpretationBox[ RowBox[{ TagBox["Failure", "SummaryHead"], "[", DynamicModuleBox[{Typeset`open$$ = False, Typeset`embedState$$ = "Ready"}, TemplateBox[{ PaneSelectorBox[{False -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}], True -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic]}, "SummaryPanel"], DynamicModuleValues:>{}], "]"}], Failure["NotTileable", <||>], Editable->False, SelectWithContents->True, Selectable->False], ",", InterpretationBox[ RowBox[{ TagBox["Failure", "SummaryHead"], "[", DynamicModuleBox[{Typeset`open$$ = False, Typeset`embedState$$ = "Ready"}, TemplateBox[{ PaneSelectorBox[{False -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}], True -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic]}, "SummaryPanel"], DynamicModuleValues:>{}], "]"}], Failure["NotTileable", <||>], Editable->False, SelectWithContents->True, Selectable->False], ",", InterpretationBox[ RowBox[{ TagBox["Failure", "SummaryHead"], "[", DynamicModuleBox[{Typeset`open$$ = False, Typeset`embedState$$ = "Ready"}, TemplateBox[{ PaneSelectorBox[{False -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}], True -> GridBox[{{ FrameBox[ StyleBox["\"\[WarningSign]\"", Directive["Message", 35], StripOnInput -> False], ContentPadding -> False, FrameStyle -> None, FrameMargins -> {{0, 0}, {0, 0}}, StripOnInput -> False], GridBox[{{ RowBox[{ TagBox[ TemplateBox[{"\"Tag\"", "\": \""}, "RowDefault"], "SummaryItemAnnotation"], "\[InvisibleSpace]", TagBox[ TagBox["\"NotTileable\"", HoldForm], "SummaryItem"]}]}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Automatic}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> { "Columns" -> {{2}}, "Rows" -> {{Automatic}}}, BaseStyle -> { ShowStringCharacters -> False, NumberMarks -> False, PrintPrecision -> 3, ShowSyntaxStyles -> False}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}, "Rows" -> {{Top}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]}, Dynamic[Typeset`open$$], ImageSize -> Automatic]}, "SummaryPanel"], DynamicModuleValues:>{}], "]"}], Failure["NotTileable", <||>], Editable->False, SelectWithContents->True, Selectable->False]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{3.864817200257325*^9, 3.864822734937818*^9, 3.864825949147044*^9}, CellLabel->"Out[2]=", CellID->64771924] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Options", "\[NonBreakingSpace]", Cell["(3)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellTags->"DefaultContent", CellID->859239780], Cell[CellGroupData[{ Cell[TextData[{ "Boundary", "\[NonBreakingSpace]", Cell["(3)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsubsection", TaggingRules->{}, CellID->784335776], Cell["\<\ Generate a tiling on a size-30 torus (i.e. a tiling with a size 30\[Times]30 \ periodic boundary):\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.864822782637945*^9, 3.8648227874265823`*^9}, 3.86785554967918*^9}, CellID->765732799], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"13", ",", "2", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["3784", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{0, 1, 1}, {1, 1, 1}}, {{1, 0, 1}, {1, 1, 1}}, {{1, 1, 0}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}}, {{0, 1, 0}, {0, 0, 0}}, {{0, 0, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 1, 0}}, {{0, 0, 0}, {1, 0, 0}}, {{1, 0, 1}, {0, 0, 0}}, {{1, 1, 1}, {0, 1, 0}}, {{0, 0, 1}, {0, 1, 1}}, {{0, 1, 0}, {1, 1, 0}}, {{1, 0, 0}, {1, 0, 1}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", "30", ",", RowBox[{"\"\\"", " ", "->", " ", "\"\\""}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}]}], "}"}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{ 3.8648077424673758`*^9, 3.8648078713338823`*^9, 3.8648090067759542`*^9, 3.864810495041288*^9, {3.864810534588628*^9, 3.864810611812933*^9}, { 3.8648176479876957`*^9, 3.8648176821138678`*^9}, {3.864818226522265*^9, 3.864818235532007*^9}}, CellLabel->"In[1]:=", CellID->545974364], Cell[BoxData[ GraphicsBox[RasterBox[CompressedData[" 1:eJxTTMoPSmJiYGCQg2JGRvwIH2DAD/ECRvxo1FWjrhoxrgIA/swDpw== "], {{0, 0}, {30, 30}}, {0, 1}], Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImageMargins->0., ImageSize->Automatic, ImageSizeRaw->Automatic, Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]], "Output", TaggingRules->{}, CellChangeTimes->{ 3.8648076682095823`*^9, {3.864807750619048*^9, 3.864807767157192*^9}, { 3.864807866496511*^9, 3.864807872237069*^9}, {3.864809004096117*^9, 3.8648090085187407`*^9}, {3.864810471606593*^9, 3.864810496252796*^9}, { 3.8648105357971287`*^9, 3.864810613136629*^9}, 3.864817671037684*^9, { 3.864818227812652*^9, 3.864818236986133*^9}, 3.864822735703259*^9, 3.8648259498154316`*^9}, CellLabel->"Out[1]=", CellID->549563490] }, Open ]], Cell["The minimum periodic region has size 5\[Times]6:", "Text", TaggingRules->{}, CellChangeTimes->{{3.856268797535082*^9, 3.856268810365205*^9}, { 3.856268847390514*^9, 3.8562688915966167`*^9}, {3.8562689644755774`*^9, 3.8562689984839125`*^9}, {3.864818253188829*^9, 3.864818271055575*^9}}, CellID->41600847], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"13", ",", "2", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["3784", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{0, 1, 1}, {1, 1, 1}}, {{1, 0, 1}, {1, 1, 1}}, {{1, 1, 0}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}}, {{0, 1, 0}, {0, 0, 0}}, {{0, 0, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 1, 0}}, {{0, 0, 0}, {1, 0, 0}}, {{1, 0, 1}, {0, 0, 0}}, {{1, 1, 1}, {0, 1, 0}}, {{0, 0, 1}, {0, 1, 1}}, {{0, 1, 0}, {1, 1, 0}}, {{1, 0, 0}, {1, 0, 1}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "6"}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"\"\\"", " ", "->", " ", "\"\\""}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "10"}]}], "]"}]}], "]"}]], "Input",\ TaggingRules->{}, CellChangeTimes->{{3.864818286611533*^9, 3.86481829368301*^9}, { 3.8648183530637302`*^9, 3.864818371828939*^9}, {3.864822807515646*^9, 3.864822809164167*^9}}, CellLabel->"In[2]:=", CellID->125305458], Cell[BoxData[ GraphicsBox[ RasterBox[{{1, 1, 0, 1, 1, 0}, {1, 1, 1, 1, 1, 1}, {0, 1, 0, 1, 0, 1}, {0, 0, 0, 0, 0, 0}, {1, 0, 0, 1, 0, 0}}, {{0, 0}, Offset[{60, 50}, {0, 0}]}, { 0, 1}], Frame->False, FrameLabel->{None, None}, FrameTicks->{{None, None}, {None, None}}, GridLinesStyle->Directive[ GrayLevel[0.5, 0.4]], ImageSize->{60, 50}, Method->{ "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}, PlotRange->{{0, 60}, {0, 50}}, PlotRangeClipping->True]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864818353598509*^9, 3.864818372318986*^9}, 3.864822735791499*^9, {3.864822798944693*^9, 3.8648228095784073`*^9}, 3.8648259499285884`*^9}, CellLabel->"Out[2]=", CellID->47858551] }, Open ]], Cell["Double-check that value by counting inequivalent translates:", "Text", TaggingRules->{}, CellChangeTimes->{{3.864818394177515*^9, 3.8648184066183367`*^9}, { 3.867855558983218*^9, 3.867855559262782*^9}}, CellID->958181628], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"13", ",", "2", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["3784", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{0, 1, 1}, {1, 1, 1}}, {{1, 0, 1}, {1, 1, 1}}, {{1, 1, 0}, {1, 1, 1}}, {{1, 1, 1}, {1, 0, 1}}, {{0, 1, 0}, {0, 0, 0}}, {{0, 0, 0}, {0, 0, 1}}, {{0, 0, 0}, {0, 1, 0}}, {{0, 0, 0}, {1, 0, 0}}, {{1, 0, 1}, {0, 0, 0}}, {{1, 1, 1}, {0, 1, 0}}, {{0, 0, 1}, {0, 1, 1}}, {{0, 1, 0}, {1, 1, 0}}, {{1, 0, 0}, {1, 0, 1}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Length", "@", RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", RowBox[{"{", RowBox[{"5", ",", "6"}], "}"}], ",", "All", ",", "\[IndentingNewLine]", RowBox[{"\"\\"", " ", "->", " ", "\"\\""}]}], "]"}]}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.86481831883261*^9, 3.864818337211643*^9}, { 3.864822814096786*^9, 3.86482281542472*^9}}, CellLabel->"In[3]:=", CellID->955356937], Cell[BoxData["30"], "Output", TaggingRules->{}, CellChangeTimes->{{3.864818315009467*^9, 3.864818344118064*^9}, 3.864818415270053*^9, 3.864822735876638*^9, 3.864822822633032*^9, 3.864825956424608*^9}, CellLabel->"Out[3]=", CellID->909212850] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Possible Issues", "\[NonBreakingSpace]", Cell["(2)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellTags->"DefaultContent", CellID->84863745], Cell["Templates must have the same bounding dimensions:", "Text", TaggingRules->{}, CellChangeTimes->{{3.864815498515008*^9, 3.864815510073056*^9}}, CellID->753437929], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"{", "1", "}"}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}], ",", "4"}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648148469853573`*^9, 3.864814864932003*^9}}, CellLabel->"In[1]:=", CellID->989316766], Cell[BoxData[ TemplateBox[{ "ResourceFunction", "usermessage", "\"\\!\\(\\*TemplateBox[List[StyleBox[RowBox[List[\\\"GenerateTiling\\\", \ \\\"::\\\", \\\"templates\\\"]], \\\"MessageName\\\"], \\\"\\\\\\\": \\\\\\\"\ \\\", TemplateBox[List[\\\"\\\\\\\"All input templates must have same \ dimensions a\\\\[Times]b.\\\\\\\"\\\"], \\\"RowDefault\\\"]], \ \\\"RowDefault\\\"]\\)\"", 2, 1, 1, 17819895501175866413, "Local"}, "MessageTemplate"]], "Message", "MSG", TaggingRules->{}, CellChangeTimes->{3.8648153285418673`*^9, 3.864815367536977*^9, 3.864822735960066*^9, 3.864825959025135*^9}, CellLabel->"During evaluation of In[1]:=", CellID->610620694], Cell[BoxData["$Failed"], "Output", TaggingRules->{}, CellChangeTimes->{3.864814865484605*^9, 3.864814959286886*^9, 3.864815328552164*^9, 3.8648153675473537`*^9, 3.864822735972281*^9, 3.864825959029793*^9}, CellLabel->"Out[1]=", CellID->329392075] }, Open ]], Cell["If not, it is always possible to add more blanks:", "Text", TaggingRules->{}, CellChangeTimes->{{3.86481551787565*^9, 3.864815524392147*^9}}, CellID->335201745], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{"Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[ Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "_"}], "}"}], ",", RowBox[{"{", RowBox[{"_", ",", "_"}], "}"}]}], "}"}]}], "}"}], ",", RowBox[{"{", "}"}], ",", "4"}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648148469853573`*^9, 3.864814864932003*^9}, { 3.864814895869323*^9, 3.864814898720827*^9}}, CellLabel->"In[2]:=", CellID->82883296], Cell[BoxData[ RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}], ",", RowBox[{"{", RowBox[{"1", ",", "1", ",", "1", ",", "1"}], "}"}]}], "}"}]], "Output", TaggingRules->{}, CellChangeTimes->{3.864814899059033*^9, 3.8648149624889917`*^9, 3.8648153718330317`*^9, 3.8648227359812326`*^9, 3.8648259591201344`*^9}, CellLabel->"Out[2]=", CellID->946760457] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[TextData[{ "Neat Examples", "\[NonBreakingSpace]", Cell["(2)", "ExampleCount"], "\[NonBreakingSpace]" }], "Subsection", TaggingRules->{}, CellTags->"DefaultContent", CellID->510369528], Cell["\<\ Generate a periodic tiling pattern from a complicated set of tiles:\ \>", "Text", TaggingRules->{}, CellChangeTimes->{{3.856264042708762*^9, 3.8562640721219115`*^9}, { 3.864817470993587*^9, 3.8648174956369667`*^9}}, CellTags->"DefaultContent", CellID->96430861], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"14", ",", "3", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["7096", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{0, 0, Blank[]}, {0, Blank[], 0}, {1, Blank[], Blank[]}}, {{0, 0, Blank[]}, {0, Blank[], 1}, {0, Blank[], Blank[]}}, {{0, 0, Blank[]}, {1, Blank[], 0}, {0, Blank[], Blank[]}}, {{0, 0, Blank[]}, {1, Blank[], 0}, {1, Blank[], Blank[]}}, {{0, 1, Blank[]}, {0, Blank[], 0}, {1, Blank[], Blank[]}}, {{0, 1, Blank[]}, {0, Blank[], 1}, {0, Blank[], Blank[]}}, {{0, 1, Blank[]}, {1, Blank[], 1}, {1, Blank[], Blank[]}}, {{1, 0, Blank[]}, {0, Blank[], 0}, {1, Blank[], Blank[]}}, {{1, 0, Blank[]}, {1, Blank[], 0}, {0, Blank[], Blank[]}}, {{1, 0, Blank[]}, {1, Blank[], 1}, {1, Blank[], Blank[]}}, {{1, 1, Blank[]}, {0, Blank[], 0}, {0, Blank[], Blank[]}}, {{1, 1, Blank[]}, {0, Blank[], 0}, {1, Blank[], Blank[]}}, {{1, 1, Blank[]}, {1, Blank[], 0}, {0, Blank[], Blank[]}}, {{1, 1, Blank[]}, {1, Blank[], 1}, {0, Blank[], Blank[]}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", "}"}], ",", "79", ",", RowBox[{"\"\\"", "->", "\"\\""}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "4"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"Grid", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{"Append", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ImageSize", "\[Rule]", "50"}], ",", "\[IndentingNewLine]", RowBox[{"Mesh", "->", "True"}], ",", RowBox[{"ColorRules", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"Verbatim", "[", "_", "]"}], "->", "Gray"}], "}"}]}]}], "\[IndentingNewLine]", "]"}], "&"}], "/@", "tiles"}], ",", "\"\<\>\""}], "]"}], ",", "7"}], "]"}], ",", RowBox[{"Spacings", "->", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "@", RowBox[{"Style", "[", RowBox[{ "\"\<(Gray squares in templates stand for Blank wildcards)\>\"", ",", "\[IndentingNewLine]", "Gray"}], "]"}]}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.8648173671005774`*^9, 3.864817421160036*^9}, { 3.8648174521258173`*^9, 3.864817456676399*^9}, {3.864817508717451*^9, 3.864817607641168*^9}}, CellLabel->"In[1]:=", CellID->881372481], Cell[BoxData[ TemplateBox[{ GraphicsBox[ RasterBox[CompressedData[" 1:eJzt01EKgzAQRdH3uhNXVOgS3ID7/yuGmCbNn97AQKIIosNlwOO2H5/9Jemd L1+H8lHuzmfpTC/tatRl0tdkHkAi/zshEVGRaick0uyERMokEGl2QiKq1UHs HJqdFrtHHzsuOyORdickMoKdkMgodg7NTkhETSgsO7HsjETmZCcoot8607AT Flnsnn7s0Oz6mUjsHJqdQrMzEjEbqXcKzM4zsRMU6XZCIpqJnUOzExJZ7O5H RrFzaHaiIhOyM8tOSKSeJtl1v9n9SLr5AnP4D4w= "], {{0, 0}, Offset[{316, 316}, {0, 0}]}, {0, 1}], ImageSize -> {316, 316}, PlotRange -> {{0, 316}, {0, 316}}, PlotRangeClipping -> True, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TemplateBox[{ TagBox[ GridBox[{{ GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 5}, {{1}, {2}, {3}, {2}, {3}}}, {0., 0.5, 0.5, 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 4, 5}, {{2}, {3}, {2}, {3}, {3}}}, {0.5, 0.5, 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 4, 5}, {{2}, {3}, {1}, {2}, {3}}}, {0.5, 0.5, 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 5, 6}, {{1}, {2}, {3}, {1}, {2}, {3}}}, {0., 0.5, 0.5, 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 6}, {{1}, {2}, {3}, {2}, {2}, {3}}}, {0., 0.5, 0.5, 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 4, 6}, {{2}, {3}, {2}, {3}, {2}, {3}}}, {0.5, 0.5, 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 6, 8}, {{1}, {2}, {3}, {1}, {2}, {3}, {2}, {3}}}, {0., 0.5, 0.5, 0., 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}, { GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 6}, {{1}, {2}, {3}, {2}, {1}, {3}}}, {0., 0.5, 0.5, 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 4, 6}, {{2}, {3}, {1}, {2}, {1}, {3}}}, {0.5, 0.5, 0., 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 6, 8}, {{1}, {2}, {3}, {1}, {2}, {3}, {1}, {3}}}, {0., 0.5, 0.5, 0., 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 6}, {{2}, {3}, {2}, {1}, {2}, {3}}}, {0.5, 0.5, 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 7}, {{1}, {2}, {3}, {2}, {1}, {2}, {3}}}, {0., 0.5, 0.5, 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 4, 7}, {{2}, {3}, {1}, {2}, {1}, {2}, {3}}}, {0.5, 0.5, 0., 0.5, 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 5, 8}, {{2}, {3}, {1}, {2}, {3}, {1}, {2}, {3}}}, { 0.5, 0.5, 0., 0.5, 0., 0., 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}], "Grid"], InterpretationBox[ Cell[ BoxData[ FormBox[ StyleBox["\"(Gray squares in templates stand for Blank wildcards)\"", GrayLevel[0.5], StripOnInput -> False], TextForm]], "InlineText"], Text[ Style["(Gray squares in templates stand for Blank wildcards)", GrayLevel[0.5]]]]}, "Labeled", DisplayFunction -> (GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction -> (RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", "}"}]}], "]"}]& )]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864817377902677*^9, 3.864817428904171*^9}, 3.8648175269877357`*^9, {3.864817579616647*^9, 3.8648175982394247`*^9}, 3.864822743555374*^9, 3.8648259667423325`*^9}, CellLabel->"Out[1]=", CellID->856560016] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[ InterpretationBox[Cell["\t", "ExampleDelimiter"], $Line = 0; Null]], "ExampleDelimiter", TaggingRules->{}, CellID->14107565], Cell[TextData[{ "Generate the nested pattern from ", ButtonBox["NKS, Chapter 5 (p. 219)", BaseStyle->"Hyperlink", ButtonData->{ URL["https://www.wolframscience.com/nks/p219--systems-based-on-\ constraints/"], None}, ButtonNote-> "https://www.wolframscience.com/nks/p219--systems-based-on-constraints/"], ":" }], "Text", TaggingRules->{}, CellChangeTimes->{{3.864819313994294*^9, 3.864819372285985*^9}}, CellID->617059534], Cell[CellGroupData[{ Cell[BoxData[ RowBox[{"With", "[", RowBox[{ RowBox[{"{", RowBox[{"tiles", "=", InterpretationBox[ DynamicModuleBox[{Typeset`open = False}, TemplateBox[{"List", "ListIcon", GridBox[{{ RowBox[{ TagBox["\"Head: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["List", "IconizedItem"]}]}, { RowBox[{ TagBox["\"Dimensions: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox[ RowBox[{"{", RowBox[{"12", ",", "3", ",", "3"}], "}"}], "IconizedItem"]}]}, { RowBox[{ TagBox["\"Byte count: \"", "IconizedLabel"], "\[InvisibleSpace]", TagBox["6088", "IconizedItem"]}]}}, GridBoxAlignment -> {"Columns" -> {{Left}}}, DefaultBaseStyle -> "Column", GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Dynamic[Typeset`open]}, "IconizedObject"]], {{{ Blank[], 1, Blank[]}, {1, 0, 0}, { Blank[], 0, Blank[]}}, {{ Blank[], 1, Blank[]}, {0, 1, 0}, { Blank[], 0, Blank[]}}, {{ Blank[], 1, Blank[]}, {0, 0, 1}, { Blank[], 1, Blank[]}}, {{ Blank[], 1, Blank[]}, {0, 0, 1}, { Blank[], 0, Blank[]}}, {{ Blank[], 1, Blank[]}, {0, 0, 0}, { Blank[], 1, Blank[]}}, {{ Blank[], 0, Blank[]}, {1, 1, 1}, { Blank[], 0, Blank[]}}, {{ Blank[], 0, Blank[]}, {1, 0, 1}, { Blank[], 1, Blank[]}}, {{ Blank[], 0, Blank[]}, {1, 0, 0}, { Blank[], 1, Blank[]}}, {{ Blank[], 0, Blank[]}, {0, 1, 1}, { Blank[], 1, Blank[]}}, {{ Blank[], 0, Blank[]}, {0, 1, 0}, { Blank[], 0, Blank[]}}, {{ Blank[], 0, Blank[]}, {0, 0, 1}, { Blank[], 0, Blank[]}}, {{ Blank[], 0, Blank[]}, {0, 0, 0}, { Blank[], 0, Blank[]}}}, SelectWithContents->True, Selectable->False]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{ RowBox[{ InterpretationBox[ TagBox[ DynamicModuleBox[{Typeset`open = False}, FrameBox[ PaneSelectorBox[{False->GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"], ImageSizeCache->{11., {1., 10.}}], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"], ImageSizeCache->{11., {1., 10.}}]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}], True-> GridBox[{ {GridBox[{ { PaneBox[GridBox[{ { StyleBox[ StyleBox[ AdjustmentBox["\<\"[\[FilledSmallSquare]]\"\>", BoxBaselineShift->-0.25, BoxMargins->{{0, 0}, {-1, -1}}], "ResourceFunctionIcon", FontColor->RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784]], ShowStringCharacters->False, FontFamily->"Source Sans Pro Black", FontSize->0.6538461538461539 Inherited, FontWeight->"Heavy", PrivateFontOptions->{"OperatorSubstitution"->False}], StyleBox[ RowBox[{ StyleBox["GenerateTiling", "ResourceFunctionLabel"], " "}], ShowAutoStyles->False, ShowStringCharacters->False, FontSize->Rational[12, 13] Inherited, FontColor->GrayLevel[0.1]]} }, GridBoxSpacings->{"Columns" -> {{0.25}}}], Alignment->Left, BaseStyle->{ LineSpacing -> {0, 0}, LineBreakWithin -> False}, BaselinePosition->Baseline, FrameMargins->{{3, 0}, {0, 0}}], ItemBox[ PaneBox[ TogglerBox[Dynamic[Typeset`open], {True-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeCloser"]], False-> DynamicBox[FEPrivate`FrontEndResource[ "FEBitmaps", "IconizeOpener"]]}, Appearance->None, BaselinePosition->Baseline, ContentPadding->False, FrameMargins->0], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{1, 1}, {0, 0}}], Frame->{{ RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627, 0.5], False}, {False, False}}]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings->{"Columns" -> {{0}}, "Rows" -> {{0}}}]}, { StyleBox[ PaneBox[GridBox[{ { RowBox[{ TagBox["\<\"Version (latest): \"\>", "IconizedLabel"], " ", TagBox["\<\"2.0.0\"\>", "IconizedItem"]}]}, { TagBox[ TemplateBox[{ "\"Documentation \[RightGuillemet]\"", "https://resources.wolframcloud.com/FunctionRepository/\ resources/9ccab8a8-7d8a-41ce-a17a-f3e2faa0d035/"}, "HyperlinkURL"], "IconizedItem"]} }, DefaultBaseStyle->"Column", GridBoxAlignment->{"Columns" -> {{Left}}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], Alignment->Left, BaselinePosition->Baseline, FrameMargins->{{5, 4}, {0, 4}}], "DialogStyle", FontFamily->"Roboto", FontSize->11]} }, BaselinePosition->{1, 1}, GridBoxAlignment->{ "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, GridBoxDividers->{"Columns" -> {{None}}, "Rows" -> {False, { GrayLevel[0.8]}, False}}, GridBoxItemSize->{ "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}]}, Dynamic[Typeset`open], BaselinePosition->Baseline, ImageSize->Automatic], Background->RGBColor[ 0.9686274509803922, 0.9764705882352941, 0.984313725490196], BaselinePosition->Baseline, DefaultBaseStyle->{}, FrameMargins->{{0, 0}, {1, 0}}, FrameStyle->RGBColor[ 0.8313725490196079, 0.8470588235294118, 0.8509803921568627], RoundingRadius->4]], {"FunctionResourceBox", RGBColor[ 0.8745098039215686, 0.2784313725490196, 0.03137254901960784], "GenerateTiling"}, TagBoxNote->"FunctionResourceBox"], ResourceFunction["GenerateTiling"], BoxID -> "GenerateTiling", Selectable->False], "[", RowBox[{"tiles", ",", RowBox[{"{", RowBox[{ RowBox[{"{", "1", "}"}], ",", RowBox[{"{", "1", "}"}]}], "}"}], ",", "100"}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"Frame", "\[Rule]", "False"}], ",", RowBox[{"Mesh", "\[Rule]", "None"}], ",", RowBox[{"PixelConstrained", "\[Rule]", "4"}]}], "}"}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Labeled", "[", RowBox[{ RowBox[{"Grid", "[", RowBox[{ RowBox[{"Partition", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{"ArrayPlot", "[", RowBox[{"#", ",", RowBox[{"ImageSize", "\[Rule]", "50"}], ",", "\[IndentingNewLine]", RowBox[{"Mesh", "->", "True"}], ",", RowBox[{"ColorRules", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"0", "->", "White"}], ",", RowBox[{"1", "->", "Black"}], ",", RowBox[{"_", "->", "Gray"}]}], "}"}]}]}], "\[IndentingNewLine]", "]"}], "&"}], "/@", "tiles"}], ",", "6"}], "]"}], ",", RowBox[{"Spacings", "->", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}]}], "]"}], ",", "\[IndentingNewLine]", RowBox[{"Text", "@", RowBox[{"Style", "[", RowBox[{ "\"\<(Gray squares in templates stand for Blank wildcards)\>\"", ",", "\[IndentingNewLine]", "Gray"}], "]"}]}]}], "]"}], ",", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", " ", "1"}], "}"}]}]}], "]"}]}], "]"}]], "Input", TaggingRules->{}, CellChangeTimes->{{3.864819406858918*^9, 3.864819440851*^9}, { 3.864819472605385*^9, 3.86481951973833*^9}, {3.8648196541438828`*^9, 3.864819663365323*^9}, {3.864819722235025*^9, 3.8648197462656593`*^9}}, CellLabel->"In[1]:=", CellID->410616192], Cell[BoxData[ TemplateBox[{ GraphicsBox[ RasterBox[CompressedData[" 1:eJzdlUtSAzEMBTXchCtxhBR77r+jmMRGkuWPpKcFqBI8oYLftFti3h9fH483 Ivp8vS+6wK/+7lf1EfggFvEq+FmJ7ankuNghvVb6cV4SIdciirb5s4oipJsi CuoUuL4aIkop+lwQVoeIkC5QIHJL7gIG0iMah4wEU5B2AeorETEeXAGFdoHQ Ie/XcJEHGY9GU6RBxJ1bLvIgamPDRbqvlAPTBY6Cpi5yOkTE3EUGRFFMXKRA hogpRRhEddTURaKvRMTSRZaCb7KoXET7uaKIgTAK2rkIgoiInYsYiKLYuAj1 1RBRQqF32FYkQh3VviIULGRP4QTpW5NYkSDjER1RePpKRBy7yFCcuvDoGCJO Kc5BWES7PK9AhMfFOYjxJx4MV4R3LkIUrrk41aHvyO9iCzIeldPFHkSevXsu TkDMNnVTLPtK33nIxSkFC/FTrHTwiNhcbEEkRWgudiA6IupiATJSBF3cGMcR pRTtm+E6ici5MEHGTRMubBBNkHNhggyTfS85jE1E2sUJRdbFoMOKyFJcVoT+ Qr6MCHVUgDIo2AqgIDsCNRdLCshcdI5JBM7FNacAufgFsSJgFJcR0S5xGEYE 1IWmYL/EUZCKwM6FRpHXSIreVj0C7cIkArvQHPi5EFvzj/Did17mQj1c8RQ3 CPx5sSYpoaCS58WMosrFE6RyLjRQJUb9/6hXSB1F4/jbLhrIX3fx5PgHLm6O +voGaZkaew== "], {{0, 0}, Offset[{400, 400}, {0, 0}]}, {0, 1}], ImageSize -> {400, 400}, PlotRange -> {{0, 400}, {0, 400}}, PlotRangeClipping -> True, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], TemplateBox[{ TagBox[ GridBox[{{ GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 6}, {{1}, {3}, {1}, {1}, {2}, {3}}}, {0.5, 0.5, 0., 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 6}, {{1}, {3}, {2}, {1}, {2}, {3}}}, {0.5, 0.5, 0., 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 7}, {{1}, {2}, {3}, {3}, {1}, {2}, {3}}}, {0.5, 0., 0.5, 0., 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 6}, {{1}, {3}, {3}, {1}, {2}, {3}}}, {0.5, 0.5, 0., 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 3, 6}, {{1}, {2}, {3}, {1}, {2}, {3}}}, {0.5, 0., 0.5, 0.5, 0., 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 5, 7}, {{1}, {3}, {1}, {2}, {3}, {1}, {3}}}, {0.5, 0.5, 0., 0., 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}, { GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 5, 7}, {{1}, {2}, {3}, {1}, {3}, {1}, {3}}}, {0.5, 0., 0.5, 0., 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 4, 6}, {{1}, {2}, {3}, {1}, {1}, {3}}}, {0.5, 0., 0.5, 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 3, 5, 7}, {{1}, {2}, {3}, {2}, {3}, {1}, {3}}}, {0.5, 0., 0.5, 0., 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{ Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 5}, {{1}, {3}, {2}, {1}, {3}}}, {0.5, 0.5, 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 3, 5}, {{1}, {3}, {3}, {1}, {3}}}, {0.5, 0.5, 0., 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}], GraphicsBox[{ RasterBox[ SparseArray[ Automatic, {3, 3}, 1., { 1, {{0, 2, 2, 4}, {{1}, {3}, {1}, {3}}}, {0.5, 0.5, 0.5, 0.5}}], {{0, 0}, {3, 3}}, {0, 1}], {{Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 3}, {3, 3}}, {{0, 2}, {3, 2}}, {{0, 1}, {3, 1}}, {{ 0, 0}, {3, 0}}}]}, {Antialiasing -> False, GrayLevel[ NCache[-1 + GoldenRatio, 0.6180339887498949]], LineBox[{{{0, 0}, {0, 3}}, {{1, 0}, {1, 3}}, {{2, 0}, {2, 3}}, {{ 3, 0}, {3, 3}}}]}}}, Frame -> False, FrameLabel -> {None, None}, FrameTicks -> {{None, None}, {None, None}}, GridLinesStyle -> Directive[ GrayLevel[0.5, 0.4]], ImageSize -> 50, Method -> { "DefaultBoundaryStyle" -> Automatic, "DefaultGraphicsInteraction" -> { "Version" -> 1.2, "TrackMousePosition" -> {True, False}, "Effects" -> { "Highlight" -> {"ratio" -> 2}, "HighlightPoint" -> {"ratio" -> 2}, "Droplines" -> { "freeformCursorMode" -> True, "placement" -> {"x" -> "All", "y" -> "None"}}}}, "DefaultPlotStyle" -> Automatic}]}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}], "Grid"], InterpretationBox[ Cell[ BoxData[ FormBox[ StyleBox["\"(Gray squares in templates stand for Blank wildcards)\"", GrayLevel[0.5], StripOnInput -> False], TextForm]], "InlineText"], Text[ Style["(Gray squares in templates stand for Blank wildcards)", GrayLevel[0.5]]]]}, "Labeled", DisplayFunction -> (GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction -> (RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", "}"}]}], "]"}]& )]}, "Labeled", DisplayFunction->(GridBox[{{ TagBox[ ItemBox[ PaneBox[ TagBox[#, "SkipImageSizeLevel"], Alignment -> {Center, Baseline}, BaselinePosition -> Baseline], DefaultBaseStyle -> "Labeled"], "SkipImageSizeLevel"]}, { ItemBox[#2, DefaultBaseStyle -> "LabeledLabel"]}}, GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}, AutoDelete -> False, GridBoxItemSize -> {"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, GridBoxSpacings -> {"Columns" -> {{1}}, "Rows" -> {{1}}}, BaselinePosition -> {1, 1}]& ), InterpretationFunction->(RowBox[{"Labeled", "[", RowBox[{#, ",", #2, ",", RowBox[{"{", RowBox[{"Spacings", "\[Rule]", RowBox[{"{", RowBox[{"1", ",", "1"}], "}"}]}], "}"}]}], "]"}]& )]], "Output", TaggingRules->{}, CellChangeTimes->{{3.864819426291861*^9, 3.864819442661352*^9}, { 3.864819480657029*^9, 3.8648195254038277`*^9}, {3.864819660267309*^9, 3.864819669090781*^9}, 3.864819751783318*^9, 3.864822748816868*^9, 3.8648259725321913`*^9}, CellLabel->"Out[1]=", CellID->802738673] }, Open ]] }, Open ]] }, Closed]] }, ClosingSaveDialog->False, WindowSize->Automatic, WindowMargins->Automatic, WindowTitle->"GenerateTiling | Example Notebook", Visible->False, TaggingRules->{ "Metadata" -> { "ResourceType" -> "Function", "Name" -> "GenerateTiling", "Property" -> "ExampleNotebook"}}, FrontEndVersion->"13.1 for Mac OS X x86 (64-bit) (June 16, 2022)", StyleDefinitions->Notebook[{ Cell[ StyleData[ StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb", CharacterEncoding -> "UTF-8"]]], Cell[ StyleData[All, "Working"], Editable -> True, DockedCells -> {}], Cell[ StyleData["Notebook"], Editable -> True, DockedCells -> {}, ScrollingOptions -> {"VerticalScrollRange" -> Automatic}], Cell[ StyleData[ "Section", StyleDefinitions -> StyleData["PrimaryExamplesSection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData["Subsection", StyleDefinitions -> StyleData["ExampleSection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData[ "Subsubsection", StyleDefinitions -> StyleData["ExampleSubsection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData[ "Subsubsubsection", StyleDefinitions -> StyleData["ExampleSubsubsection"]], Editable -> True, ShowGroupOpener -> "Inline", WholeCellGroupOpener -> True], Cell[ StyleData["Text", StyleDefinitions -> StyleData["ExampleText"]], Editable -> True]}, Visible -> False, FrontEndVersion -> "13.1 for Mac OS X x86 (64-bit) (June 16, 2022)", StyleDefinitions -> "PrivateStylesheetFormatting.nb"] ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{ "DefaultContent"->{ Cell[627, 23, 197, 8, 70, "Subsection",ExpressionUUID->"16deb584-d92e-42f9-852b-07706dd0bae2", CellTags->"DefaultContent", CellID->279727361], Cell[21430, 576, 257, 5, 70, "Text",ExpressionUUID->"3e493cd1-67dd-4ab4-b8a8-92e42e2fb600", CellTags->"DefaultContent", CellID->512168029], Cell[102203, 2519, 188, 8, 70, "Subsection",ExpressionUUID->"c7862f47-b4c0-4ac0-b423-bc2c8f2b78ba", CellTags->"DefaultContent", CellID->513869560], Cell[102394, 2529, 271, 7, 70, "Text",ExpressionUUID->"f9a42bcc-c394-4595-b2a1-194419f61b15", CellTags->"DefaultContent", CellID->907666835], Cell[164987, 4017, 190, 8, 70, "Subsection",ExpressionUUID->"daf0884b-dae9-4413-bea7-a5f854a0863b", CellTags->"DefaultContent", CellID->859239780], Cell[198562, 4859, 197, 8, 70, "Subsection",ExpressionUUID->"49a1decb-b2b9-48f4-80f8-2b8789268d09", CellTags->"DefaultContent", CellID->84863745], Cell[215887, 5321, 196, 8, 70, "Subsection",ExpressionUUID->"22aa300b-27d9-4dd1-ad95-1eb6bd5cbb05", CellTags->"DefaultContent", CellID->510369528], Cell[216086, 5331, 277, 7, 70, "Text",ExpressionUUID->"3dafb501-0fea-4369-9516-6778f25efae4", CellTags->"DefaultContent", CellID->96430861]} } *) (*CellTagsIndex CellTagsIndex->{ {"DefaultContent", 289163, 7054} } *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[627, 23, 197, 8, 70, "Subsection",ExpressionUUID->"16deb584-d92e-42f9-852b-07706dd0bae2", CellTags->"DefaultContent", CellID->279727361], Cell[827, 33, 193, 4, 70, "Text",ExpressionUUID->"10975f10-3104-41e7-a49f-4fa103d888f1", CellID->848888257], Cell[CellGroupData[{ Cell[1045, 41, 7466, 187, 70, "Input",ExpressionUUID->"55ff876b-020f-4e55-aa09-be58b248e940", CellID->714828949], Cell[8514, 230, 741, 18, 70, "Output",ExpressionUUID->"2bd1c7f6-854c-498e-8660-5612d70622d0", CellID->699937031] }, Open ]], Cell[CellGroupData[{ Cell[9292, 253, 145, 4, 70, "ExampleDelimiter",ExpressionUUID->"5d137455-1dd0-4be2-a9c7-d9085f41a6c7", CellID->2016696111], Cell[9440, 259, 249, 6, 70, "Text",ExpressionUUID->"5d1a84c1-b35c-4907-9f00-414d79a0dcc2", CellID->356300994], Cell[CellGroupData[{ Cell[9714, 269, 8186, 198, 70, "Input",ExpressionUUID->"7f241c9b-da06-4f75-9756-ac61c4ea1020", CellID->416008876], Cell[17903, 469, 3332, 95, 70, "Output",ExpressionUUID->"714cb1c4-18f0-446b-a4d2-19dbac13ed9b", CellID->852863177] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[21284, 570, 143, 4, 70, "ExampleDelimiter",ExpressionUUID->"6e00c125-65aa-4a94-bdf6-e2c0fe1bdb9d", CellID->14107562], Cell[21430, 576, 257, 5, 70, "Text",ExpressionUUID->"3e493cd1-67dd-4ab4-b8a8-92e42e2fb600", CellTags->"DefaultContent", CellID->512168029], Cell[CellGroupData[{ Cell[21712, 585, 8396, 211, 70, "Input",ExpressionUUID->"0d5ec8db-d822-4b66-9820-f70d4c2a0c9c", CellID->359746122], Cell[30111, 798, 1413, 31, 70, "Output",ExpressionUUID->"77b9de50-9595-4ef3-8bee-8f77ca2afa2a", CellID->918374088] }, Open ]], Cell[31539, 832, 1161, 32, 70, "Text",ExpressionUUID->"35ea1c24-bd53-4988-b5a9-be3268ad591e", CellID->868970757], Cell[CellGroupData[{ Cell[32725, 868, 9207, 233, 70, "Input",ExpressionUUID->"a0849343-e9a7-4669-aa48-4d273e5d724b", CellID->775865682], Cell[41935, 1103, 8002, 159, 70, "Output",ExpressionUUID->"56cfa023-f8da-446b-b727-f1fd128826a2", CellID->89588579] }, Open ]], Cell[49952, 1265, 371, 8, 70, "Text",ExpressionUUID->"f26b892f-fc4a-4a2f-be31-e12c4b69a394", CellID->667907404], Cell[CellGroupData[{ Cell[50348, 1277, 9587, 246, 70, "Input",ExpressionUUID->"bcff43a0-17f3-4b05-9819-44bbd310f1dc", CellID->9502071], Cell[59938, 1525, 5932, 126, 70, "Output",ExpressionUUID->"2e543064-83d8-47b7-a6a4-dbc13c261b2d", CellID->610914188] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[65919, 1657, 143, 4, 70, "ExampleDelimiter",ExpressionUUID->"7d76d65f-5a78-484d-9b12-10b1e3aa4b41", CellID->14107563], Cell[66065, 1663, 212, 4, 70, "Text",ExpressionUUID->"77c74809-c2a1-4fae-9741-08502cd671cd", CellID->295611003], Cell[CellGroupData[{ Cell[66302, 1671, 11426, 280, 70, "Input",ExpressionUUID->"be392def-cbb0-4da6-8dc8-38fee097dc97", CellID->320857703], Cell[77731, 1953, 7418, 153, 70, "Output",ExpressionUUID->"05a4e4e8-ca7a-4def-94b7-ac4394aa5288", CellID->844591674] }, Open ]], Cell[85164, 2109, 169, 3, 70, "Text",ExpressionUUID->"32860e0c-079c-4ab1-90fa-0dff35427822", CellID->727395058], Cell[CellGroupData[{ Cell[85358, 2116, 10208, 251, 70, "Input",ExpressionUUID->"0dcf6846-7eb7-48d4-a683-ee9a71142736", CellID->130252101], Cell[95569, 2369, 6573, 143, 70, "Output",ExpressionUUID->"c5d3baa1-d9b3-47a5-8106-6e37244c476a", CellID->334403499] }, Open ]] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell[102203, 2519, 188, 8, 70, "Subsection",ExpressionUUID->"c7862f47-b4c0-4ac0-b423-bc2c8f2b78ba", CellTags->"DefaultContent", CellID->513869560], Cell[102394, 2529, 271, 7, 70, "Text",ExpressionUUID->"f9a42bcc-c394-4595-b2a1-194419f61b15", CellTags->"DefaultContent", CellID->907666835], Cell[CellGroupData[{ Cell[102690, 2540, 10990, 263, 70, "Input",ExpressionUUID->"df66aa09-94ce-41f3-9c67-9cafadd15a41", CellID->251372788], Cell[113683, 2805, 17795, 388, 70, "Output",ExpressionUUID->"820a3d8f-7529-4acb-98fd-cc40e338ab91", CellID->53467947] }, Open ]], Cell[CellGroupData[{ Cell[131515, 3198, 143, 4, 70, "ExampleDelimiter",ExpressionUUID->"31a23ec7-1ed8-4153-a081-bad95f367e31", CellID->14107564], Cell[131661, 3204, 352, 10, 70, "Text",ExpressionUUID->"b430890e-bfc2-47a0-8102-fa8e86aa7f6c", CellID->16002939], Cell[CellGroupData[{ Cell[132038, 3218, 10667, 264, 70, "Input",ExpressionUUID->"56206002-4b81-46f6-9bee-fd3568dd3329", CellID->879643092], Cell[142708, 3484, 2558, 64, 70, "Output",ExpressionUUID->"ef05bf69-5127-43cb-9b0d-7c775c99d7bf", CellID->323466370] }, Open ]], Cell[145281, 3551, 689, 17, 70, "Text",ExpressionUUID->"4852b038-5aac-47d1-b7ee-d4d624c245b5", CellID->46993719], Cell[CellGroupData[{ Cell[145995, 3572, 9143, 228, 70, "Input",ExpressionUUID->"480ed0e4-c221-4936-aa9c-f75adfc78fef", CellID->421932251], Cell[155141, 3802, 9785, 208, 70, "Output",ExpressionUUID->"872b84e4-02c5-4c4e-a293-ca3bc77a8aaf", CellID->64771924] }, Open ]] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[164987, 4017, 190, 8, 70, "Subsection",ExpressionUUID->"daf0884b-dae9-4413-bea7-a5f854a0863b", CellTags->"DefaultContent", CellID->859239780], Cell[CellGroupData[{ Cell[165202, 4029, 165, 7, 70, "Subsubsection",ExpressionUUID->"8418f257-d506-41ca-a6a7-ef19bbd24c3b", CellID->784335776], Cell[165370, 4038, 254, 7, 70, "Text",ExpressionUUID->"0492660c-d2d2-4ed2-9924-7b16c294ce79", CellID->765732799], Cell[CellGroupData[{ Cell[165649, 4049, 10024, 240, 70, "Input",ExpressionUUID->"89148f4a-be06-41a4-b9c6-e24725fb94dd", CellID->545974364], Cell[175676, 4291, 1264, 31, 70, "Output",ExpressionUUID->"864cd563-76ce-4634-9cfb-69c7eb56cf36", CellID->549563490] }, Open ]], Cell[176955, 4325, 318, 5, 70, "Text",ExpressionUUID->"a50d46be-1273-48db-aa77-60808c2ec51a", CellID->41600847], Cell[CellGroupData[{ Cell[177298, 4334, 10007, 239, 70, "Input",ExpressionUUID->"3471112a-a301-4fab-871d-6017452b178b", CellID->125305458], Cell[187308, 4575, 1074, 28, 70, "Output",ExpressionUUID->"56293ef3-9ba9-4ac0-bba1-6495f36e8bac", CellID->47858551] }, Open ]], Cell[188397, 4606, 232, 4, 70, "Text",ExpressionUUID->"a39d1431-30bb-44eb-90a4-5dc2e1414518", CellID->958181628], Cell[CellGroupData[{ Cell[188654, 4614, 9591, 230, 70, "Input",ExpressionUUID->"b25311a0-2f4b-461c-86b1-8961d7ab5aa1", CellID->955356937], Cell[198248, 4846, 253, 6, 70, "Output",ExpressionUUID->"0f7841ba-5bee-4640-89c9-68fc46edc170", CellID->909212850] }, Open ]] }, Closed]] }, Closed]], Cell[CellGroupData[{ Cell[198562, 4859, 197, 8, 70, "Subsection",ExpressionUUID->"49a1decb-b2b9-48f4-80f8-2b8789268d09", CellTags->"DefaultContent", CellID->84863745], Cell[198762, 4869, 170, 3, 70, "Text",ExpressionUUID->"702b4c49-a66d-4914-9a3b-524c962071e9", CellID->753437929], Cell[CellGroupData[{ Cell[198957, 4876, 7504, 192, 70, "Input",ExpressionUUID->"e490874a-efec-4a19-8743-cdeb052f98f9", CellID->989316766], Cell[206464, 5070, 665, 13, 70, "Message",ExpressionUUID->"a2020de5-1b1a-42dc-ad16-38c98e1a410f", CellID->610620694], Cell[207132, 5085, 256, 6, 70, "Output",ExpressionUUID->"94251fb0-58ff-4c94-8446-d94ff3bf27ea", CellID->329392075] }, Open ]], Cell[207403, 5094, 169, 3, 70, "Text",ExpressionUUID->"8b6a3fbb-1d5a-4a6b-8d50-252a5aeef2d6", CellID->335201745], Cell[CellGroupData[{ Cell[207597, 5101, 7666, 197, 70, "Input",ExpressionUUID->"5113b41d-ee2e-4982-82b4-a2665c0eee21", CellID->82883296], Cell[215266, 5300, 572, 15, 70, "Output",ExpressionUUID->"3a59937b-64af-4f4c-9d20-c0563094047f", CellID->946760457] }, Open ]] }, Closed]], Cell[CellGroupData[{ Cell[215887, 5321, 196, 8, 70, "Subsection",ExpressionUUID->"22aa300b-27d9-4dd1-ad95-1eb6bd5cbb05", CellTags->"DefaultContent", CellID->510369528], Cell[216086, 5331, 277, 7, 70, "Text",ExpressionUUID->"3dafb501-0fea-4369-9516-6778f25efae4", CellTags->"DefaultContent", CellID->96430861], Cell[CellGroupData[{ Cell[216388, 5342, 12752, 331, 70, "Input",ExpressionUUID->"72404c64-c2a9-4047-bed3-e365afe96ad5", CellID->881372481], Cell[229143, 5675, 23657, 511, 70, "Output",ExpressionUUID->"0020f92f-9245-4717-b0e0-731597b2fc99", CellID->856560016] }, Open ]], Cell[CellGroupData[{ Cell[252837, 6191, 143, 4, 70, "ExampleDelimiter",ExpressionUUID->"7aafe69f-529f-425c-a551-7478fa013f2c", CellID->14107565], Cell[252983, 6197, 440, 13, 70, "Text",ExpressionUUID->"c543aeea-be5a-4cdf-a75f-a11041c648f5", CellID->617059534], Cell[CellGroupData[{ Cell[253448, 6214, 12600, 325, 70, "Input",ExpressionUUID->"568522c6-98ff-4fd8-ae83-2e66364a72d8", CellID->410616192], Cell[266051, 6541, 21228, 457, 70, "Output",ExpressionUUID->"91e3a2be-8db3-45ee-9865-d6fc03b6d080", CellID->802738673] }, Open ]] }, Open ]] }, Closed]] } ] *) (* End of internal cache information *)