6 steps wm6884wm6884 signature 23→43 rule {{{1, 2, 3}, {4, 5, 6}} -> {{7, 7, 2}, {7, 2, 3}, {5, 3, 7}, {1, 6, 7}}} {{{1, 2, 3}, {4, 5, 6}} -> {{7, 7, 2}, {7, 2, 3}, {5, 3, 7}, {1, 6, 7}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{7,7,2},{7,2,3},{5,3,7},{1,6,7}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{7,7,2},{7,2,3},{5,3,7},{1,6,7}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,3},{4,5,6}}{{7,7,2},{7,2,3},{5,3,7},{1,6,7}}},{{1,1,1},{1,1,1}},11,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]-1+t2Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]t2Result after 6 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},Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],Cycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]