Universe 86337 from The Wolfram Physics Project

21 steps

wm86337`wm86337`

signature

3₂→5₂

rule

{{{1, 2}, {1, 2}, {3, 1}} -> {{1, 1}, {1, 4}, {2, 1}, {2, 4}, {4, 3}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}},{{1,1},{1,1},{1,1}},6,"StatesPlotsList"]

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

Event-by-event evolution:

[◼]	WolframModel

[{{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]

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

Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}},{{1,1},{1,1},{1,1}},23,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-8-y.[n.]+y.[1+n.]-y.[2+n.]-y.[3+n.]+y.[7+n.]-y.[9+n.]+y.[10+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]6,y.[6]8,y.[7]10,y.[8]12,y.[9]14,y.[10]17,y.[11]20[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-15-y.[n.]+y.[1+n.]-y.[2+n.]-y.[3+n.]+y.[7+n.]-y.[9+n.]+y.[10+n.]0,y.[1]3,y.[2]5,y.[3]7,y.[4]9,y.[5]13,y.[6]17,y.[7]21,y.[8]25,y.[9]29,y.[10]35,y.[11]41[t]

Result after

generations:

WolframModel[

]

["FinalStatePlot"]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]



Layered rendering:

WolframModel[

]

["LayeredCausalGraph"]

Causal graph distance matrix:

MatrixPlotTransposeGraphDistanceMatrix

WolframModel[

]

["CausalGraph"],



Final State Properties

Hypergraph adjacency matrix:

MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,

WolframModel[

]

["FinalState"],



Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],



Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,



Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],



Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4

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

Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

MatrixPlotExp[-(distanceMatrix/.0None)],



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],



Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"87|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{1,2},{3,1}}{{1,1},{1,4},{2,1},{2,4},{4,3}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"87|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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