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Random Rules

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urules24=Import["/Users/sw/Dropbox/Physics/Data/22-24-2x0-unioned-summary.wxf"];

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SeedRandom[6783];GraphicsGrid[Partition[WolframModelPlot[List@@@EdgeList[#]]&/@Take[Select[ParallelMapMonitored[UndirectedGraph[Rule@@@WolframModel[#,{{0,0},{0,0}},8,"FinalState"],GraphLayout->"SpringElectricalEmbedding"]&,#Rule&/@RandomSample[urules24,150]],EdgeCount[#]>10&&ConnectedGraphQ[#]&],60],10],ImageSizeFull]

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List@@@EdgeList[#]&/@Take[Select[ParallelMapMonitored[UndirectedGraph[Rule@@@WolframModel[#,{{0,0},{0,0}},8,"FinalState"],GraphLayout->"SpringElectricalEmbedding"]&,#Rule&/@RandomSample[urules24,150]],EdgeCount[#]>10&&ConnectedGraphQ[#]&],60]

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SeedRandom[6785];GraphicsGrid[Partition[Take[Select[ParallelMapMonitored[UndirectedGraph[Rule@@@WolframModel[#,{{0,0},{0,0}},8,"FinalState"],GraphLayout->"SpringElectricalEmbedding"]&,#Rule&/@RandomSample[urules24,150]],EdgeCount[#]>10&&ConnectedGraphQ[#]&],252],UpTo[10]],ImageSizeFull]

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GraphicsGrid[Partition[ParallelMapMonitored[WolframModel[#[[1]],#[[2]],#[[3]],"FinalStatePlot"]&,{{{{1,2},{1,3}}{{1,2},{1,4},{2,4},{4,3}},{{0,0},{0,0}},12},{{{1,2},{1,3}}{{1,4},{1,4},{2,4},{3,2}},{{0,0},{0,0}},10},{{{1,2},{1,3}}{{2,2},{2,4},{1,4},{3,4}},{{0,0},{0,0}},10},{{{1,2},{1,3}}{{2,3},{2,4},{3,4},{1,4}},{{0,0},{0,0}},10},{{{1,2},{1,3}}{{2,3},{2,4},{3,4},{4,1}},{{0,0},{0,0}},12},{{{1,2},{1,3}}{{2,4},{2,1},{4,1},{4,3}},{{0,0},{0,0}},9},{{{1,2},{1,3}}{{2,4},{2,4},{1,4},{3,4}},{{0,0},{0,0}},10},{{{1,2},{1,3}}{{2,4},{2,4},{2,1},{3,4}},{{0,0},{0,0}},10},{{{1,2},{1,3}}{{4,1},{1,4},{4,2},{4,3}},{{0,0},{0,0}},12},{{{1,2},{2,3}}{{1,2},{2,1},{4,1},{4,3}},{{0,0},{0,0}},10},{{{1,2},{2,3}}{{1,3},{1,4},{3,4},{3,2}},{{0,0},{0,0}},10},{{{1,2},{2,3}}{{2,3},{2,4},{3,4},{1,2}},{{0,0},{0,0}},9}}],4],ImageSizeFull]

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{{{{1,2,3},{3,4,5}}{{6,3,5},{3,1,6},{6,2,4}},{{0,0,0},{0,0,0}},19},{{{1,2,3},{2,4,5}}{{4,5,4},{5,6,1},{3,2,6}},{{0,0,0},{0,0,0}},18},{{{1,2,3},{4,5,3}}{{2,6,3},{2,6,4},{1,5,2}},{{0,0,0},{0,0,0}},20},{{{1,2,3},{2,4,5}}{{1,4,6},{6,4,3},{2,1,5}},{{0,0,0},{0,0,0}},19},{{{1,2,3},{3,4,5}}{{2,6,2},{3,2,4},{5,6,1}},{{0,0,0},{0,0,0}},19},{{{1,2,3},{1,4,5}}{{2,5,6},{5,1,3},{3,4,6}},{{0,0,0},{0,0,0}},16},{{{1,2,3},{4,2,5}}{{2,6,3},{6,1,2},{1,4,2}},{{0,0,0},{0,0,0}},19},{{{1,2,3},{4,3,5}}{{5,2,5},{5,1,6},{4,5,6}},{{0,0,0},{0,0,0}},19},{{{1,2,3},{4,2,5}}{{6,3,4},{6,2,4},{3,4,5}},{{0,0,0},{0,0,0}},20},{{{1,2,3},{4,3,5}}{{3,5,2},{5,2,4},{2,1,6}},{{0,0,0},{0,0,0}},18},{{{1,2,3},{4,3,5}}{{6,3,1},{1,4,3},{2,6,5}},{{0,0,0},{0,0,0}},35},{{{1,2,3},{2,4,5}}{{6,5,1},{1,5,4},{3,2,6}},{{0,0,0},{0,0,0}},80},{{{1,2,3},{4,2,5}}{{6,3,4},{6,3,1},{6,4,2}},{{0,0,0},{0,0,0}},150},{{{1,2,3},{1,4,5}}{{2,6,1},{6,4,1},{2,4,3}},{{0,0,0},{0,0,0}},150},{{{1,2,3},{4,5,3}}{{6,6,2},{6,4,6},{5,1,2}},{{0,0,0},{0,0,0}},150},{{{1,1,2},{3,4,1}}{{4,4,3},{5,4,5},{5,2,1}},{{0,0,0},{0,0,0}},150},{{{1,2,3},{4,2,5}}{{6,3,1},{3,6,4},{1,2,6}},{{0,0,0},{0,0,0}},150},{{{1,2,3},{1,4,5}}{{3,3,6},{6,6,5},{4,5,6}},{{0,0,0},{0,0,0}},100},{{{1,2,2},{2,3,4}}{{4,3,3},{4,1,5},{2,4,5}},{{0,0,0},{0,0,0}},100},{{{1,2,3},{1,4,5}}{{2,3,6},{2,3,6},{5,2,6}},{{0,0,0},{0,0,0}},100}}[[10]]

2,3  3,3 ??

Messy Example Case

Tech Document

Planarity

Example of a particle

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