Universe 9464 from The Wolfram Physics Project

22 steps

wm9464`wm9464`

signature

3₂→4₂

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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

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

Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{2,3},{2,5},{3,5},{2,4}}},{{1,1},{1,1},{1,1}},39,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-5(-4+n.)(-3+n.)(-2+n.)(-1+n.)-2(-10+n.)(-6+n.)3671-764n.+5

y.[n.]+440280-208652n.+32040

-1588

y.[1+n.]+(-10+n.)(-6+n.)3671-764n.+5

y.[4+n.]+-220140+104326n.-16020

+794

y.[5+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]5,y.[6]7,y.[7]9,y.[8]11,y.[9]13,y.[10]16,y.[11]19,y.[12]23,y.[13]27,y.[14]35[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

-8+5

(-1)

-5

(-)

-5



-3

(-1)

-3

(-)

+3



1+t

(-1)

+

(-)

-



t/4

(-1)

t/4

(-)

t/4



t/4

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},{1,3},{1,4}}{{2,3},{2,5},{3,5},{2,4}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"188|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{1,3},{1,4}}{{2,3},{2,5},{3,5},{2,4}}},{{1,1},{1,1},{1,1}},<|"MaxEvents"188|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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