1 steps wm8678wm8678 signature 2213→3223 rule {{{1, 2, 3}, {4, 4}, {5, 3}} -> {{3, 2, 4}, {3, 4, 5}, {1, 5}, {2, 6}, {7, 8}}} {{{1, 2, 3}, {4, 4}, {5, 3}} -> {{3, 2, 4}, {3, 4, 5}, {1, 5}, {2, 6}, {7, 8}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,3},{4,4},{5,3}}{{3,2,4},{3,4,5},{1,5},{2,6},{7,8}}},{{1,1,1},{1,1},{1,1}},1,"StatesPlotsList"],Event-by-event evolution:[◼]WolframModel[{{{1,2,3},{4,4},{5,3}}{{3,2,4},{3,4,5},{1,5},{2,6},{7,8}}},{{1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"EventsStatesPlotsList"],Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,3},{4,4},{5,3}}{{3,2,4},{3,4,5},{1,5},{2,6},{7,8}}},{{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],0.00.20.40.60.81.00.00.51.01.52.0Successive 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},Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],Cycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]