Ornamental patters made from parts of circle and cosine wave
Sándor Kabai
The geometric patterns are created with segments of circle and cosine curve.
The geometric patterns are created with segments of circle and cosine curve.
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(*Creatingpetalfromsegmentsofacircle*)
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s2=ParametricPlot3D[{Sin[x],Cos[x],0},{x,0,2Pi}][[1]];s21=ParametricPlot3D[{Sin[x],Cos[x],0},{x,Pi/2,0.618},PlotStyle->{Yellow,Tube[0.04]}][[1]];sa=Translate[s21,{-Sin[0.618],0,0}];sb=Rotate[sa,Pi,{0,1,0}];p1={sa,sb};Graphics3D[{s2,s21,p1},FaceGrids->All,ViewPoint->{0,0,100},ImageSize->200]
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petal1=Table[Rotate[Translate[{sa,sb},{0,1.63,0}],i2Pi/13,{0,0,1}],{i,13}];Graphics3D[{petal1},FaceGrids->All,ViewPoint->{0,0,100},ImageSize->200]
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petals=Table[Rotate[Scale[petal1,1.2^i{1,1,1},{0,0,0}],i2Pi/13,{0,0,1}],{i,8}];Graphics3D[{petals},ViewPoint->{0,0,100},Boxed->False,SphericalRegion->True]
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fi=GoldenRatio;petals1=Table[Rotate[Scale[petal1,1.43^i{1,1,1},{0,0,0}],i2Pi/26,{0,0,1}],{i,8}];Graphics3D[{petals1},ViewPoint->{0,0,100},Boxed->False,SphericalRegion->True]
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petals1=Table[Rotate[Scale[petal1,1.25^i{1,1,1},{0,0,0}],ifi2Pi/26,{0,0,1}],{i,8}];Graphics3D[{petals1},ViewPoint->{0,0,100},Boxed->False,SphericalRegion->True]
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(*Selectapartofthewave,formaunitwithitsmirrorimage,andthenplacetheunitaroundacircle.Explorethepossiblepatternsbyvaryingthecirclediameterandthesizeoftheunit*)sin1=ParametricPlot3D[{x,1.2Cos[x]+0.5,0},{x,-Pi,3Pi}][[1]];sin2=ParametricPlot3D[{x,1.2Cos[x]+0.5,0},{x,-1,1.37Pi},PlotStyle->{Pink,Tube[0.13]}][[1]];sin3=Rotate[sin2,Pi,{1,0,0}];Graphics3D[{sin1,sin2,sin3},Axes->True,FaceGrids->All,ViewPoint->{0,0,100},SphericalRegion->True]
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p1={sin2,sin3};sp=Sphere[{0,0,0},0.1];p2=Table[Rotate[Translate[p1,{4,0,0}],i2Pi/20,{0,0,1}],{i,20}];cin=ParametricPlot3D[3.2{Sin[x],Cos[x],0},{x,0,2Pi},PlotStyle->{Yellow,Tube[0.08]}][[1]];Graphics3D[{cin,p2},ViewPoint->{0,0,100},SphericalRegion->True,Boxed->False]
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sin1a=ParametricPlot3D[{x,1.2Cos[x]+0.5,0},{x,-Pi,3Pi}][[1]];sin2a=ParametricPlot3D[{x,1.2Cos[x]+0.5,0},{x,-1,2.65Pi},PlotStyle->{Yellow,Tube[0.13]}][[1]];sin3a=Rotate[sin2a,Pi,{1,0,0}];Graphics3D[{sin1a,sin2a,sin3a},Axes->True,FaceGrids->All,ViewPoint->{0,0,100},SphericalRegion->True]
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p1a={sin2a,sin3a};p2a=Table[Rotate[Translate[p1a,{4.5,0,0}],i2Pi/20,{0,0,1}],{i,20}];cina=ParametricPlot3D[3.6{Sin[x],Cos[x],0},{x,0,2Pi},PlotStyle->{Yellow,Tube[0.2]}][[1]];Graphics3D[{cina,p2a},ViewPoint->{0,0,100},SphericalRegion->True,Boxed->False,ImageSize->400]
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p1a={sin2a,sin3a};p2a=Table[Rotate[Translate[p1a,{2.8,0,0}],i2Pi/24,{0,0,1}],{i,24}];cina=ParametricPlot3D[2.1{Sin[x],Cos[x],0},{x,0,2Pi},PlotStyle->{Pink,Tube[0.1]}][[1]];Graphics3D[{cina,p2a},ViewPoint->{0,0,100},SphericalRegion->True,Boxed->False,ImageSize->400]
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p1a={sin2a,sin3a};p2a=Table[Rotate[Translate[p1a,{7,0,0}],i2Pi/24,{0,0,1}],{i,24}];cina=ParametricPlot3D[6{Sin[x],Cos[x],0},{x,0,2Pi},PlotStyle->{Cyan,Tube[0.1]}][[1]];Graphics3D[{cina,p2a},ViewPoint->{0,0,100},SphericalRegion->True,Boxed->False,ImageSize->400]
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