Universe 8279 from The Wolfram Physics Project

59 steps

wm8279`wm8279`

signature

2₃→3₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{6,1,1},{7,6,8},{7,1,4}}},{{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]4,y.[3]6,y.[4]10,y.[5]13,y.[6]17,y.[7]22,y.[8]27,y.[9]33,y.[10]38,y.[11]44,y.[12]49,y.[13]54,y.[14]59,y.[15]65,y.[16]70,y.[17]75,y.[18]80,y.[19]86,y.[20]91,y.[21]96,y.[22]101,y.[23]107,y.[24]112,y.[25]117,y.[26]122,y.[27]128,y.[28]133,y.[29]138,y.[30]143,y.[31]149,y.[32]154,y.[33]159,y.[34]164,y.[35]170,y.[36]175,y.[37]180,y.[38]185,y.[39]191,y.[40]196,y.[41]201,y.[42]206,y.[43]212,y.[44]217,y.[45]222,y.[46]227,y.[47]233,y.[48]238,y.[49]243,y.[50]248,y.[51]254,y.[52]259,y.[53]264,y.[54]269,y.[55]275,y.[56]280,y.[57]285,y.[58]290,y.[59]296,y.[60]301,y.[61]306,y.[62]311,y.[63]317,y.[64]322,y.[65]327,y.[66]332,y.[67]338[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

wm8279wm8279

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8279`wm8279`