Basic Evolution
Basic Evolution
Basic evolution:
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Event-by-event evolution:
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Vertex and edge counts:
{vertexCountList,edgeCountList}=[{{{1,1}}{{1,1},{1,2},{2,2}}},{{1,1}},14,{"VertexCountList","EdgeCountList"}];
ListLogPlot{vertexCountList,edgeCountList},
Symbolic expression for vertex count:
FindSequenceFunction[vertexCountList,t]
-1+t
2
Symbolic expression for edge count:
FindSequenceFunction[edgeCountList,t]
-1+
t
2
Result after generations:
6
Causal Graph
Causal Graph
Causal graph:
Layered rendering:
Causal graph distance matrix:
MatrixPlotTransposeGraphDistanceMatrix["CausalGraph"],
Final State Properties
Final State Properties
Hypergraph adjacency matrix:
MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,["FinalState"],
Vertex degree distribution:
HistogramValuesCountsCatenateUnion/@["FinalState"],
Neighborhood volumes (ignoring directedness of connections):
volumes=Values["FinalState"],All,Automatic;
Effective dimension versus radius:
Successive neighborhood balls around a random vertex:
Distance matrix:
Distribution of distances in the graph:
Spreading of Effects
Spreading of Effects
Causal graph adjacency matrix:
Neighborhood volumes in causal graph:
Other Evolution Orders
Other Evolution Orders
Random evolutions:
Different deterministic evolution orders:
Graph Features of States
Graph Features of States
Cycle properties: