Universe 7835 from The Wolfram Physics Project

102 steps

wm7835`wm7835`

signature

2₃→3₃

rule

{{{1, 2, 1}, {3, 2, 4}} -> {{3, 1, 3}, {2, 5, 1}, {5, 4, 2}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{3,1,3},{2,5,1},{5,4,2}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"]





Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{3,1,3},{2,5,1},{5,4,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]

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

Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{3,1,3},{2,5,1},{5,4,2}}},{{1,1,1},{1,1,1}},500,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-23952+12700n.-2330

+140

+-20976+14150n.-3665

+430

-19

y.[n.]+(-9+n.)-2664+1454n.-279

+19

y.[1+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]5,y.[6]7,y.[7]8,y.[8]9,y.[9]10,y.[10]12[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-26952+14300n.-2630

+160

+-20976+14150n.-3665

+430

-19

y.[n.]+(-9+n.)-2664+1454n.-279

+19

y.[1+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]5,y.[5]6,y.[6]8,y.[7]9,y.[8]10,y.[9]11,y.[10]13[t]

Result after

102

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},{3,2,4}}{{3,1,3},{2,5,1},{5,4,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"197|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{3,1,3},{2,5,1},{5,4,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"197|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

