101 steps wm1932wm1932 signature 23→33 rule {{{1, 2, 1}, {2, 3, 4}} -> {{5, 3, 5}, {1, 3, 5}, {2, 4, 4}}} {{{1, 2, 1}, {2, 3, 4}} -> {{5, 3, 5}, {1, 3, 5}, {2, 4, 4}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,1},{2,3,4}}{{5,3,5},{1,3,5},{2,4,4}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,1},{2,3,4}}{{5,3,5},{1,3,5},{2,4,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,1},{2,3,4}}{{5,3,5},{1,3,5},{2,4,4}}},{{1,1,1},{1,1,1}},500,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]DifferenceRootFunction{y.,n.},5+(4-n.)y.[n.]+(-5+n.)y.[1+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]5,y.[6]7[t]Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]DifferenceRootFunction{y.,n.},6+(4-n.)y.[n.]+(-5+n.)y.[1+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]5,y.[5]6,y.[6]8[t]Result after 101 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[{{{1,2,1},{2,3,4}}{{5,3,5},{1,3,5},{2,4,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2,1},{2,3,4}}{{5,3,5},{1,3,5},{2,4,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"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]]