1 steps wm37269wm37269 signature 2223→8243 rule {{{1, 2, 3}, {4, 5, 6}, {2, 5}, {5, 2}} -> {{7, 1, 8}, {9, 3, 10}, {11, 4, 12}, {13, 6, 14}, {7, 13}, {13, 7}, {8, 10}, {10, 8}, {9, 11}, {11, 9}, {12, 14}, {14, 12}}} {{{1, 2, 3}, {4, 5, 6}, {2, 5}, {5, 2}} -> {{7, 1, 8}, {9, 3, 10}, {11, 4, 12}, {13, 6, 14}, {7, 13}, {13, 7}, {8, 10}, {10, 8}, {9, 11}, {11, 9}, {12, 14}, {14, 12}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{13,7},{8,10},{10,8},{9,11},{11,9},{12,14},{14,12}}},{{1,1,1},{1,1,1},{1,1},{1,1}},1,"StatesPlotsList"],Event-by-event evolution:[◼]WolframModel[{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{13,7},{8,10},{10,8},{9,11},{11,9},{12,14},{14,12}}},{{1,1,1},{1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"EventsStatesPlotsList"],Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{13,7},{8,10},{10,8},{9,11},{11,9},{12,14},{14,12}}},{{1,1,1},{1,1,1},{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[{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{13,7},{8,10},{10,8},{9,11},{11,9},{12,14},{14,12}}},{{1,1,1},{1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2,3},{4,5,6},{2,5},{5,2}}{{7,1,8},{9,3,10},{11,4,12},{13,6,14},{7,13},{13,7},{8,10},{10,8},{9,11},{11,9},{12,14},{14,12}}},{{1,1,1},{1,1,1},{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]]]FindSpanningTree[UndirectedGraph[graph]]