6 steps wm2998wm2998 signature 23→43 rule {{{1, 2, 3}, {4, 5, 6}} -> {{1, 5, 7}, {1, 7, 4}, {2, 5, 4}, {8, 7, 5}}} {{{1, 2, 3}, {4, 5, 6}} -> {{1, 5, 7}, {1, 7, 4}, {2, 5, 4}, {8, 7, 5}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"],,,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},11,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]DifferenceRootFunction{y.,n.},-2y.[n.]+y.[1+n.]0,y.[1]1,y.[2]3,y.[3]7[t]Symbolic 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},Other Evolution OrdersRandom evolutions:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"63|>,"FinalStatePlot","EventOrderingFunction""Random"][◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,FinalStatePlot,EventOrderingFunctionRandom]Different deterministic evolution orders:[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"63|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{OldestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelOldestEdge],[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{LeastOldEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastOldEdge],[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{LeastRecentEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastRecentEdge],[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{NewestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelNewestEdge],[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{RuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelRuleOrdering],[◼]WolframModel[{{{1,2,3},{4,5,6}}{{1,5,7},{1,7,4},{2,5,4},{8,7,5}}},{{1,1,1},{1,1,1}},MaxEvents63,EventOrderingFunction{ReverseRuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelReverseRuleOrdering]Graph Features of Statesgraph=[◼]HypergraphToGraphWolframModel[]["FinalState"];HistogramClosenessCentrality[graph],Cycle properties:EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlotHistogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]FindSpanningTree[UndirectedGraph[graph]]