17 steps wm8386wm8386 signature 22→32 rule {{{1, 1}, {1, 2}} -> {{2, 2}, {2, 2}, {1, 3}}} {{{1, 1}, {1, 2}} -> {{2, 2}, {2, 2}, {1, 3}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,1},{1,2}}{{2,2},{2,2},{1,3}}},{{1,1},{1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,1},{1,2}}{{2,2},{2,2},{1,3}}},{{1,1},{1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,1},{1,2}}{{2,2},{2,2},{1,3}}},{{1,1},{1,1}},38,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]16(3+3)-54+1513+t32+91+t32+383+t32-183+513+t323+31+t323+83+t323+18t-12/32-32/32-151/32t-12/32-32/32+63t-12/32-32/32+51/323t-12/32-32/32-82/323t-12/32-32/32+18t-12/32+32/32-122/32t-12/32+32/32+63t-12/32+32/32-101/323t-12/32+32/32+42/323t-12/32+32/32Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]16(3+3)-36+1513+t32+91+t32+383+t32-123+513+t323+31+t323+83+t323+18t-12/32-32/32-151/32t-12/32-32/32+63t-12/32-32/32+51/323t-12/32-32/32-82/323t-12/32-32/32+18t-12/32+32/32-122/32t-12/32+32/32+63t-12/32+32/32-101/323t-12/32+32/32+42/323t-12/32+32/32Result after 17 generations:WolframModel[]["FinalStatePlot"]Causal GraphCausal graph:WolframModel[]"CausalGraph",Rule[]Layered rendering:WolframModel[]["LayeredCausalGraph"]Causal graph distance matrix:MatrixPlotTransposeGraphDistanceMatrixWolframModel[]["CausalGraph"],Final State PropertiesHypergraph adjacency matrix:MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,WolframModel[]["FinalState"],Vertex degree distribution:HistogramValuesCountsCatenateUnion/@WolframModel[]["FinalState"],Neighborhood volumes (ignoring directedness of connections):volumes=[◼]RaggedMeanAroundValues[◼]HypergraphNeighborhoodVolumesWolframModel[]["FinalState"],All,Automatic;ListLogLogPlotvolumes,Effective dimension versus radius:ListLinePlot[◼]LogDifferences[volumes],Successive neighborhood balls around a random vertex: [◼]HypergraphNeighborhoodsWolframModel[]["FinalState"],4{,,,}Distance matrix:distanceMatrix=GraphDistanceMatrixUndirectedGraph[◼]HypergraphToGraphWolframModel[]["FinalState"];MatrixPlotExp[-(distanceMatrix/.0None)],Distribution of distances in the graph:HistogramFlatten[distanceMatrix],Spreading of EffectsCausal graph adjacency matrix:MatrixPlotAdjacencyMatrixWolframModel[]["CausalGraph"],Neighborhood volumes in causal graph:ListLogLogPlotValues[◼]GraphNeighborhoodVolumesWolframModel[]["CausalGraph"],{1},Other Evolution OrdersRandom evolutions:[◼]WolframModel[{{{1,1},{1,2}}{{2,2},{2,2},{1,3}}},{{1,1},{1,1}},<|"MaxEvents"188|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,1},{1,2}}{{2,2},{2,2},{1,3}}},{{1,1},{1,1}},<|"MaxEvents"188|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"},,,,,Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],Cycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]