1 steps wm9848wm9848 signature 22→1222→32 rule {{{1, 2}, {2, 1}} -> {{3, 3}}, {{1, 2}, {3, 2}} -> {{4, 1}, {4, 2}, {1, 2}}} {{{1, 2}, {2, 1}} -> {{3, 3}}, {{1, 2}, {3, 2}} -> {{4, 1}, {4, 2}, {1, 2}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2},{2,1}}{{3,3}},{{1,2},{3,2}}{{4,1},{4,2},{1,2}}},{{1,1},{1,1}},1,"StatesPlotsList"],Event-by-event evolution:[◼]WolframModel[{{{1,2},{2,1}}{{3,3}},{{1,2},{3,2}}{{4,1},{4,2},{1,2}}},{{1,1},{1,1}},<|"MaxEvents"1|>,"EventsStatesPlotsList"],Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2},{2,1}}{{3,3}},{{1,2},{3,2}}{{4,1},{4,2},{1,2}}},{{1,1},{1,1}},1,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesResult after 1 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},{2,1}}{{3,3}},{{1,2},{3,2}}{{4,1},{4,2},{1,2}}},{{1,1},{1,1}},<|"MaxEvents"1|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2},{2,1}}{{3,3}},{{1,2},{3,2}}{{4,1},{4,2},{1,2}}},{{1,1},{1,1}},<|"MaxEvents"1|>,"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]]]0.20.40.60.81.0-1.0-0.50.00.51.0FindSpanningTree[UndirectedGraph[graph]]