5 steps wm2818wm2818 signature 13→33 rule {{{1, 2, 1}} -> {{3, 3, 3}, {3, 1, 3}, {1, 3, 2}}} {{{1, 2, 1}} -> {{3, 3, 3}, {3, 1, 3}, {1, 3, 2}}}
make editable copy download notebook Basic EvolutionBasic evolution:[◼]WolframModel[{{{1,2,1}}{{3,3,3},{3,1,3},{1,3,2}}},{{1,1,1}},5,"StatesPlotsList"],,,,,Event-by-event evolution:[◼]WolframModel[{{{1,2,1}}{{3,3,3},{3,1,3},{1,3,2}}},{{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"],,,,,,Vertex and edge counts:{vertexCountList,edgeCountList}=[◼]WolframModel[{{{1,2,1}}{{3,3,3},{3,1,3},{1,3,2}}},{{1,1,1}},11,{"VertexCountList","EdgeCountList"}];ListLogPlot{vertexCountList,edgeCountList},verticesedgesSymbolic expression for vertex count:FindSequenceFunction[vertexCountList,t]Fibonacci[t,2]Symbolic expression for edge count:FindSequenceFunction[edgeCountList,t]-2+22+2t(1-2)+2t(1-2)-2t(1+2)-2t(1+2)2(1+2)Result after 5 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[{{{1,2,1}}{{3,3,3},{3,1,3},{1,3,2}}},{{1,1,1}},<|"MaxEvents"69|>,"FinalStatePlot","EventOrderingFunction""Random"]Different deterministic evolution orders:[◼]WolframModel[{{{1,2,1}}{{3,3,3},{3,1,3},{1,3,2}}},{{1,1,1}},<|"MaxEvents"69|>,"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]]