9 steps wm7279wm7279 signature 22→42 rule {{{1, 2}, {2, 3}} -> {{3, 4}, {3, 4}, {3, 1}, {1, 4}}} {{{1, 2}, {2, 3}} -> {{3, 4}, {3, 4}, {3, 1}, {1, 4}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2},{2,3}}{{3,4},{3,4},{3,1},{1,4}}},{{1,1},{1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2},{2,3}}{{3,4},{3,4},{3,1},{1,4}}},{{1,1},{1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2},{2,3}}{{3,4},{3,4},{3,1},{1,4}}},{{1,1},{1,1}},19,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},SequenceIconverticesedgesResult after 9 generations:WolframModel[]["FinalStatePlot"]Causal GraphCausal graph:WolframModel[]"CausalGraph",Rule[]Layered rendering:WolframModel[]["LayeredCausalGraph"]Causal graph distance matrix:MatrixPlotTransposeGraphDistanceMatrixWolframModel[]["CausalGraph"],ListIconContents cannot be rendered at this time; please try again laterFinal State PropertiesHypergraph adjacency matrix:MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,WolframModel[]["FinalState"],ListIconContents cannot be rendered at this time; please try again laterVertex degree distribution:HistogramValuesCountsCatenateUnion/@WolframModel[]["FinalState"],ListIconContents cannot be rendered at this time; please try again laterNeighborhood volumes (ignoring directedness of connections):volumes=[◼]RaggedMeanAroundValues[◼]HypergraphNeighborhoodVolumesWolframModel[]["FinalState"],All,Automatic;ListLogLogPlotvolumes,ListIconContents cannot be rendered at this time; please try again laterEffective dimension versus radius:ListLinePlot[◼]LogDifferences[volumes],ListIconContents cannot be rendered at this time; please try again laterSuccessive neighborhood balls around a random vertex: [◼]HypergraphNeighborhoodsWolframModel[]["FinalState"],4{,,,}Distance matrix:distanceMatrix=GraphDistanceMatrixUndirectedGraph[◼]HypergraphToGraphWolframModel[]["FinalState"];MatrixPlotExp[-(distanceMatrix/.0None)],ListIconContents cannot be rendered at this time; please try again laterDistribution of distances in the graph:HistogramFlatten[distanceMatrix],ListIconContents cannot be rendered at this time; please try again laterSpreading of EffectsCausal graph adjacency matrix:MatrixPlotAdjacencyMatrixWolframModel[]["CausalGraph"],ListIconContents cannot be rendered at this time; please try again laterNeighborhood volumes in causal graph:ListLogLogPlotValues[◼]GraphNeighborhoodVolumesWolframModel[]["CausalGraph"],{1},ListIconContents cannot be rendered at this time; please try again laterOther Evolution OrdersRandom evolutions:[◼]WolframModel[{{{1,2},{2,3}}{{3,4},{3,4},{3,1},{1,4}}},{{1,1},{1,1}},<|"MaxEvents"94|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2},{2,3}}{{3,4},{3,4},{3,1},{1,4}}},{{1,1},{1,1}},<|"MaxEvents"94|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}{,,,,,}Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],ListIconContents cannot be rendered at this time; please try again laterCycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]