Universe 8874 from The Wolfram Physics Project

50 steps

wm8874
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`wm8874`

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2₃→4₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{6,7,7},{6,2,1},{7,5,3},{8,7,9}}},{{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},{6,2,1},{7,5,3},{8,7,9}}},{{1,1,1},{1,1,1}},60,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-3135130+1631850n.-170108

+(-11+n.)(-4+n.)(-313+172n.)y.[n.]+-17928+7407n.-477

y.[1+n.]+3170-1650n.+172

y.[2+n.]+3170-1650n.+172

y.[3+n.]+3170-1650n.+172

y.[4+n.]+3170-1650n.+172

y.[5+n.]+3170-1650n.+172

y.[6+n.]+3170-1650n.+172

y.[7+n.]+3170-1650n.+172

y.[8+n.]+16942-13913n.+3065

-172

y.[9+n.]+(-11+n.)(-1918+649n.)y.[10+n.]0,y.[1]1,y.[2]5,y.[3]13,y.[4]21,y.[5]28,y.[6]35,y.[7]43,y.[8]51,y.[9]58,y.[10]65,y.[11]73,y.[12]80,y.[13]87,y.[14]95,y.[15]102,y.[16]110,y.[17]118,y.[18]125,y.[19]132,y.[20]140,y.[21]148[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

wm8874✖copy to clipboardwm8874

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8874
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`wm8874`