Universe 8622 from The Wolfram Physics Project

34 steps

wm8622`wm8622`

signature

2₃→4₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{2,6,7},{7,5,1},{4,7,1}}},{{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.},-6-y.[n.]+y.[1+n.]0,y.[1]1,y.[2]3,y.[3]7,y.[4]11,y.[5]17,y.[6]23,y.[7]29,y.[8]35,y.[9]41,y.[10]47,y.[11]53,y.[12]59,y.[13]64,y.[14]70,y.[15]76,y.[16]82,y.[17]88,y.[18]94,y.[19]100,y.[20]106,y.[21]111,y.[22]117,y.[23]123,y.[24]129,y.[25]135,y.[26]141,y.[27]146,y.[28]152,y.[29]158,y.[30]163,y.[31]169,y.[32]175,y.[33]181,y.[34]187,y.[35]193,y.[36]198[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-6n.-y.[n.]+2y.[1+n.]0,y.[1]2,y.[2]4,y.[3]8,y.[4]12[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

wm8622wm8622

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8622`wm8622`