Universe 9956 from The Wolfram Physics Project

62 steps

wm9956`wm9956`

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2₃→3₃

rule

{{{1, 2, 2}, {3, 4, 5}} -> {{6, 7, 7}, {8, 5, 7}, {9, 5, 2}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{6,7,7},{8,5,7},{9,5,2}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"]





Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{6,7,7},{8,5,7},{9,5,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{6,7,7},{8,5,7},{9,5,2}}},{{1,1,1},{1,1,1}},69,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-5-y.[n.]+y.[1+n.]0,y.[1]1,y.[2]5,y.[3]7,y.[4]11,y.[5]15,y.[6]20,y.[7]25,y.[8]30,y.[9]36,y.[10]41,y.[11]47,y.[12]52,y.[13]57,y.[14]62,y.[15]68,y.[16]73,y.[17]78,y.[18]83,y.[19]89,y.[20]94,y.[21]99,y.[22]104,y.[23]110,y.[24]115,y.[25]120,y.[26]125,y.[27]131,y.[28]136,y.[29]141,y.[30]146,y.[31]152,y.[32]157,y.[33]162,y.[34]167,y.[35]173,y.[36]178,y.[37]183,y.[38]188,y.[39]194,y.[40]199,y.[41]204,y.[42]209,y.[43]215,y.[44]220,y.[45]225,y.[46]230,y.[47]236,y.[48]241,y.[49]246,y.[50]251,y.[51]257,y.[52]262,y.[53]267,y.[54]272,y.[55]278,y.[56]283,y.[57]288,y.[58]293,y.[59]299,y.[60]304,y.[61]309,y.[62]314,y.[63]320,y.[64]325,y.[65]330,y.[66]335,y.[67]341[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-44+11n.+3

+-28+19n.-3

y.[n.]+38-23n.+3

y.[1+n.]0,y.[1]2[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





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},



Graph Features of States

graph=

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

HistogramClosenessCentrality[graph],



Cycle properties:

EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlot

Histogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]

FindSpanningTree[UndirectedGraph[graph]]

‹ Registry of Notable Universe Models

wm9956wm9956

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm9956`wm9956`