Universe 8842 from The Wolfram Physics Project

5 steps

wm8842`wm8842`

signature

1₃→4₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2,1}}{{1,3,1},{1,3,2},{2,4,2},{4,3,3}}},{{1,1,1}},5,"StatesPlotsList"]

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Event-by-event evolution:

[◼]	WolframModel

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

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Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,1}}{{1,3,1},{1,3,2},{2,4,2},{4,3,3}}},{{1,1,1}},14,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

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

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-5-2y.[n.]+y.[1+n.]0,y.[1]1,y.[2]4[t]

Result after

generations:

WolframModel[

]

["FinalStatePlot"]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]

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Layered rendering:

WolframModel[

]

["LayeredCausalGraph"]

Causal graph distance matrix:

MatrixPlotTransposeGraphDistanceMatrix

WolframModel[

]

["CausalGraph"],

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Final State Properties

Hypergraph adjacency matrix:

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

WolframModel[

]

["FinalState"],

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Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],

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Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,

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Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],

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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)],

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Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

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Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},

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Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2,1}}{{1,3,1},{1,3,2},{2,4,2},{4,3,3}}},{{1,1,1}},<|"MaxEvents"46|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,1}}{{1,3,1},{1,3,2},{2,4,2},{4,3,3}}},{{1,1,1}},<|"MaxEvents"46|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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