allsigs={{11},{12},{13},{22},{11,11},{14},{23},{11,12},{12,11},{15},{24},{33},{11,13},{13,11},{11,22},{12,12},{12,21},{21,12},{22,11},{11,11,11},{16},{25},{34},{11,14},{14,11},{11,23},{12,13},{12,31},{13,12},{13,21},{21,13},{23,11},{31,12},{12,22},{22,12},{11,11,12},{11,12,11},{12,11,11}};
In[]:=
MultiwaySystem[{"A""AA","A""B"},"A",5]
In[]:=
{{A},{AA,B},{AAA,AB,BA},{AAAA,AAB,ABA,BAA,BB},{AAAAA,AAAB,AABA,ABAA,ABB,BAAA,BAB,BBA},{AAAAAA,AAAAB,AAABA,AABAA,AABB,ABAAA,ABAB,ABBA,BAAAA,BAAB,BABA,BBAA,BBB}}
Out[]=
gm=MultiwaySystem[{"A""AA","A""B"},"A",5,"StatesGraph"]
In[]:=
Out[]=
VertexList[gm]
In[]:=
{A,AA,B,AAA,AB,BA,AAAA,AAB,ABA,BAA,BB,AAAAA,AAAB,AABA,ABAA,ABB,BAAA,BAB,BBA,AAAAAA,AAAAB,AAABA,AABAA,AABB,ABAAA,ABAB,ABBA,BAAAA,BAAB,BABA,BBAA,BBB}
Out[]=
GraphNeighborhoodVolumes[gm,{"A"},Automatic]
In[]:=
A{1,3,6,11,19,32}
Out[]=
GraphNeighborhoodVolumes[MultiwaySystem[{"A""AA","A""B"},"A",10,"StatesGraph"],{"A"},Automatic]
In[]:=
A{1,3,6,11,19,32,53,87,142,231,375}
Out[]=

Basic function:

MWGrowth[rule_,inits_,t_Integer]:=GraphNeighborhoodVolumes[MultiwaySystem[rule,inits,t,"StatesGraph"],inits,Automatic]
In[]:=
EnumerateSubstitutionSystemRules[{11,12},2]
In[]:=
Out[]=
ParallelMapMonitored[MWGrowth[#,StringTuples["AB",3],15]&,EnumerateSubstitutionSystemRules[{11,12},2]]
In[]:=
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<20>, <25>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68548++) & )}]
is not a valid vertex.
(kernel 65)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<232>, <330>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$71005++) & )}]
is not a valid vertex.
(kernel 68)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1152>, <2595>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68821++) & )}]
is not a valid vertex.
(kernel 67)
Out[]=
​
ParallelMapMonitored[#({#,Differences[#],Ratios[#]}&[MeanAround/@Transpose[Values[MWGrowth[#,StringTuples["AB",3],15]]]])&,EnumerateSubstitutionSystemRules[{11,12},2]]
In[]:=
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<20>, <25>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68567++) & )}]
is not a valid vertex.
(kernel 65)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<232>, <330>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$71024++) & )}]
is not a valid vertex.
(kernel 68)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1152>, <2595>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68840++) & )}]
is not a valid vertex.
(kernel 67)
Out[]=
Last[%524]
In[]:=
Out[]=
If[Length[#[[2,1]]]<5,Nothing,First[#](ListPlot[#,PlotTheme"Minimal",PlotRange{0,Automatic},Ticks{None,Automatic}]&/@Last[#])]&/@%524
In[]:=
Out[]=
ParallelEvaluate[Off[BreadthFirstScan::inv]]
In[]:=
{Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null}
Out[]=
Map[If[Length[#[[2,1]]]<5,Nothing,First[#](ListPlot[#,PlotTheme"Minimal",PlotRange{0,Automatic},Ticks{None,Automatic}]&/@Last[#])]&/@ParallelMapMonitored[TimeConstrained[#({#,Differences[#],Ratios[#]}&[MeanAround/@Transpose[Values[MWGrowth[#,StringTuples["AB",3],15]]]]),15]&,EnumerateSubstitutionSystemRules[#,2]]]&/@Take[allsigs,3]
In[]:=
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<7>, <0>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$71131++) & )}]
is not a valid vertex.
(kernel 68)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<232>, <330>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$71149++) & )}]
is not a valid vertex.
(kernel 68)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1152>, <2595>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68965++) & )}]
is not a valid vertex.
(kernel 67)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<20>, <25>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68675++) & )}]
is not a valid vertex.
(kernel 65)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<20>, <25>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$54154++) & )}]
is not a valid vertex.
(kernel 61)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<232>, <330>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$71167++) & )}]
is not a valid vertex.
(kernel 68)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1272>, <2805>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$60990++) & )}]
is not a valid vertex.
(kernel 63)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1152>, <2595>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$62910++) & )}]
is not a valid vertex.
(kernel 62)
BreadthFirstScan::inv:The argument BBB in
BreadthFirstScan[Graph[<1152>, <2580>], BBB, {DiscoverVertex -> ((If[Greater[<<2>>], Throw[<<2>>]]; If[Greater[<<2>>], CompoundExpression[<<2>>]]; FunctionRepository`$844172c161324b318cee0545f605f2b2`vertexCounter$68693++) & )}]
is not a valid vertex.
(kernel 65)
Part
:Part specification $Aborted〚2,1〛 is longer than depth of object.
During evaluation of In[537]:=
{Map[{}],Map[{}],Map[{}]}
Out[]=
allsigs
In[]:=
Out[]=
ParallelMapMonitored[TimeConstrained[#({#,Differences[#],Ratios[#]}&[MeanAround/@Transpose[Values[MWGrowth[#,StringTuples["AB",3],15]]]]),15]&,EnumerateSubstitutionSystemRules[{12},2]]
In[]:=
{{AAA}{{0.88±0.13},{},{}},{AAB}{{0.88±0.13},{},{}},{ABB}{{0.88±0.13},{},{}}}
Out[]=
CellPrint[ExpressionCell[(If[Length[#[[2,1]]]<5,Nothing,First[#](ListPlot[#,PlotTheme"Minimal",PlotRange{0,Automatic},Ticks{None,Automatic}]&/@Last[#])]&/@ParallelMapMonitored[TimeConstrained[#({#,Differences[#],Ratios[#]}&[MeanAround/@Transpose[Values[MWGrowth[#,StringTuples["AB",3],15]]]]),5]&,EnumerateSubstitutionSystemRules[#,2]]),"Output"]]&/@Take[allsigs,5];
In[]:=
{}
{}
Part
:Part specification $Aborted〚2,1〛 is longer than depth of object.
{}
{}
{}
CellPrint[ExpressionCell[(If[Length[#[[2,1]]]<5,Nothing,First[#](ListPlot[#,PlotTheme"Minimal",PlotRange{0,Automatic},Ticks{None,Automatic}]&/@Last[#])]&/@ParallelMapMonitored[TimeConstrained[#({#,Differences[#],Ratios[#]}&[MeanAround/@Transpose[Values[MWGrowth[#,StringTuples["AB",3],15]]]]),5]&,EnumerateSubstitutionSystemRules[#,2]]),"Output"]]&/@Drop[allsigs,5];
In[]:=
Part
:Part specification $Aborted〚2,1〛 is longer than depth of object.
Part
:Part specification $Aborted〚2,1〛 is longer than depth of object.
Part
:Part specification $Aborted〚2,1〛 is longer than depth of object.
General
:Further output of Part::partd will be suppressed during this calculation.
{}
{}
{}
{}
{}
{}
{}
{}
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 82)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 83)
{}
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 82)
{}
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 83)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 82)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 84)
{}
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 70)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 78)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 70)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 80)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 84)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 82)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 84)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 70)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 83)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 82)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 76)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with sequential evaluation.
(kernel 80)
ParallelMap::subpar:Parallel computations cannot be nested; proceeding with s