Map[RulePlot[WolframModel[#],VertexLabelsAutomatic]&,Catenate[Last/@{{1,3,2}{{{1,2,3},{4,3,5}}{{6,3,1},{3,7,8},{9,4,3}},{{1,2,3},{4,3,5}}{{2,6,7},{5,6,7},{3,1,4}},{{1,2,3},{1,4,5}}{{1,6,7},{8,6,7},{9,3,4}},{{1,2,3},{4,3,5}}{{6,3,3},{5,2,7},{2,7,5}},{{1,2,3},{4,3,5}}{{6,1,4},{6,7,8},{9,2,5}},{{1,2,2},{1,3,3}}{{4,5,1},{6,1,7},{2,8,9}},{{1,2,3},{4,3,2}}{{1,5,5},{2,6,6},{3,7,7}}},{2,1,3}{{{1,1,2},{3,4,1}}{{2,2,5},{6,6,5},{4,3,2}},{{1,1,2},{2,2,3}}{{2,2,4},{2,5,6},{7,2,6}},{{1,2,3},{2,1,4}}{{1,5,6},{5,2,7},{8,9,4}},{{1,1,2},{3,4,2}}{{5,6,4},{6,7,3},{8,9,1}}},{2,3,1}{},{3,1,2}{},{3,2,1}{{{1,2,3},{4,2,5}}{{6,2,7},{6,8,9},{10,11,7}},{{1,2,1},{2,3,2}}{{3,4,3},{5,6,1},{1,7,8}},{{1,2,3},{3,4,5}}{{6,7,1},{7,8,9},{5,9,6}},{{1,2,3},{3,4,5}}{{3,6,3},{4,7,2},{8,7,9}},{{1,2,1},{2,3,2}}{{4,5,4},{5,2,5},{6,5,6}},{{1,2,3},{4,2,5}}{{2,6,2},{3,6,1},{3,7,1}},{{1,2,3},{3,4,5}}{{6,7,1},{6,3,8},{5,7,8}}}}]]

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If you reverse the state, you get the same evolution.....

Basic question: what operations commute with evolution? [Global symmetries]

EnumerateWolframModelRules[{{2,2}}{{3,2}}];

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psamp=Function[perm,perm->Pick[%368,ParallelMapMonitored[(FindCanonicalWolframModel[Map[#[[perm]]&,#,{2}]]===#)&,%368]]]/@Rest[Permutations[Range[2]]]

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Local symmetry

WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},(Reverse/@{{x,y},{x,z}}){{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},5,"StatesPlotsList"]

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WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},(Reverse/@{{x,y},{x,z}}){{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},8,"StatesPlotsList"]

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WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},(Reverse/@{{x,y},{x,z}})(Reverse/@{{x,z},{x,w},{y,w},{z,w}})},{{0,0},{0,0}},8,"StatesPlotsList"]

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