10 steps wm9473wm9473 signature 32→52 rule {{{1, 1}, {2, 3}, {3, 4}} -> {{4, 4}, {4, 4}, {2, 4}, {2, 4}, {1, 5}}} {{{1, 1}, {2, 3}, {3, 4}} -> {{4, 4}, {4, 4}, {2, 4}, {2, 4}, {1, 5}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,1},{2,3},{3,4}}{{4,4},{4,4},{2,4},{2,4},{1,5}}},{{1,1},{1,1},{1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,1},{2,3},{3,4}}{{4,4},{4,4},{2,4},{2,4},{1,5}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,1},{2,3},{3,4}}{{4,4},{4,4},{2,4},{2,4},{1,5}}},{{1,1},{1,1},{1,1}},11,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},SequenceIconverticesedgesResult after 10 generations:WolframModel[]["FinalStatePlot"]Causal GraphCausal graph:WolframModel[]"CausalGraph",Rule[]Layered rendering:WolframModel[]["LayeredCausalGraph"]Causal graph distance matrix:MatrixPlotTransposeGraphDistanceMatrixWolframModel[]["CausalGraph"],ListIconFinal State PropertiesHypergraph adjacency matrix:MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,WolframModel[]["FinalState"],ListIconVertex degree distribution:HistogramValuesCountsCatenateUnion/@WolframModel[]["FinalState"],ListIconNeighborhood volumes (ignoring directedness of connections):volumes=[◼]RaggedMeanAroundValues[◼]HypergraphNeighborhoodVolumesWolframModel[]["FinalState"],All,Automatic;ListLogLogPlotvolumes,ListIconEffective dimension versus radius:ListLinePlot[◼]LogDifferences[volumes],ListIconSuccessive neighborhood balls around a random vertex: [◼]HypergraphNeighborhoodsWolframModel[]["FinalState"],4,,,Distance matrix:distanceMatrix=GraphDistanceMatrixUndirectedGraph[◼]HypergraphToGraphWolframModel[]["FinalState"];MatrixPlotExp[-(distanceMatrix/.0None)],ListIconDistribution of distances in the graph:HistogramFlatten[distanceMatrix],ListIconSpreading of EffectsCausal graph adjacency matrix:MatrixPlotAdjacencyMatrixWolframModel[]["CausalGraph"],ListIconNeighborhood volumes in causal graph:ListLogLogPlotValues[◼]GraphNeighborhoodVolumesWolframModel[]["CausalGraph"],{1},ListIconGraph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],ListIconCycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]