60 steps wm8713wm8713 signature 23→33 rule {{{1, 2, 1}, {3, 4, 5}} -> {{2, 5, 2}, {1, 6, 2}, {4, 7, 6}}} {{{1, 2, 1}, {3, 4, 5}} -> {{2, 5, 2}, {1, 6, 2}, {4, 7, 6}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,1},{3,4,5}}{{2,5,2},{1,6,2},{4,7,6}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,1},{3,4,5}}{{2,5,2},{1,6,2},{4,7,6}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,1},{3,4,5}}{{2,5,2},{1,6,2},{4,7,6}}},{{1,1,1},{1,1,1}},68,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]DifferenceRootFunction{y.,n.},29-21n.+y.[n.]+y.[1+n.]+y.[2+n.]+y.[3+n.]0,y.[1]1,y.[2]3,y.[3]5,y.[4]9,y.[5]12,y.[6]17,y.[7]22,y.[8]27,y.[9]33,y.[10]37,y.[11]43,y.[12]48[t]Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]DifferenceRootFunction{y.,n.},-44+11n.+32n.+-28+19n.-32n.y.[n.]+38-23n.+32n.y.[1+n.]0,y.[1]2[t]Result after 64 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]]