12 steps wm5492wm5492 signature 23→33 rule {{{1, 2, 3}, {4, 2, 5}} -> {{1, 5, 1}, {1, 5, 4}, {6, 5, 2}}} {{{1, 2, 3}, {4, 2, 5}} -> {{1, 5, 1}, {1, 5, 4}, {6, 5, 2}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,3},{4,2,5}}{{1,5,1},{1,5,4},{6,5,2}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,3},{4,2,5}}{{1,5,1},{1,5,4},{6,5,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,3},{4,2,5}}{{1,5,1},{1,5,4},{6,5,2}}},{{1,1,1},{1,1,1}},21,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},SequenceIconverticesedgesResult after 12 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},ListIconOther Evolution OrdersRandom evolutions:[◼]WolframModel[{{{1,2,3},{4,2,5}}{{1,5,1},{1,5,4},{6,5,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"148|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2,3},{4,2,5}}{{1,5,1},{1,5,4},{6,5,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"148|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"},,,,,Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],ListIconCycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]