34 steps wm9353wm9353 signature 23→43 rule {{{1, 1, 2}, {3, 4, 5}} -> {{6, 6, 7}, {1, 8, 6}, {4, 1, 8}, {8, 5, 4}}} {{{1, 1, 2}, {3, 4, 5}} -> {{6, 6, 7}, {1, 8, 6}, {4, 1, 8}, {8, 5, 4}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,1,2},{3,4,5}}{{6,6,7},{1,8,6},{4,1,8},{8,5,4}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,1,2},{3,4,5}}{{6,6,7},{1,8,6},{4,1,8},{8,5,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,1,2},{3,4,5}}{{6,6,7},{1,8,6},{4,1,8},{8,5,4}}},{{1,1,1},{1,1,1}},36,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]-1+t∏K[1]=1DifferenceRootFunction{y.,n.},1602+1385n.-11312n.+-192+208n.-482n.y.[n.]+777-2724n.+11792n.y.[1+n.]0,y.[1]4[K[1]]Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]DifferenceRootFunction{y.,n.},4+6n.+(2-n.)y.[n.]+(-4+n.)y.[1+n.]0,y.[1]2,y.[2]4,y.[3]8,y.[4]14,y.[5]20[t]Result after 34 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},Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],Cycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]