Universe 1137 from The Wolfram Physics Project

4 steps

wm1137`wm1137`

signature

1₃→4₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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

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Event-by-event evolution:

[◼]	WolframModel

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

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Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1,2}}{{2,2,2},{2,1,2},{1,2,3},{3,3,1}}},{{1,1,1}},9,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-3y.[n.]+y.[1+n.]0,y.[1]1,y.[2]2[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-4-3y.[n.]+y.[1+n.]0,y.[1]1,y.[2]4[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"],

ListIcon



Final State Properties

Hypergraph adjacency matrix:

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

WolframModel[

]

["FinalState"],

ListIcon



Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],

ListIcon

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Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,

ListIcon

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Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],

ListIcon

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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)],

ListIcon



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

ListIcon

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Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],

ListIcon



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},

ListIcon

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Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,1,2}}{{2,2,2},{2,1,2},{1,2,3},{3,3,1}}},{{1,1,1}},<|"MaxEvents"53|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,1,2}}{{2,2,2},{2,1,2},{1,2,3},{3,3,1}}},{{1,1,1}},<|"MaxEvents"53|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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