Universe 8525 from The Wolfram Physics Project

50 steps

wm8525`wm8525`

signature

2₃→3₃

rule

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

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{7,2,1},{4,5,1}}},{{1,1,1},{1,1,1}},51,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-13(-20+n.)(-9+n.)(-5+n.)-9375419075239573200768+9877714264143695865808n.-3556937973251339593610

+576383755535804882925

-34392474171923758642

+636950234077864127

-14(-29+n.)(-21+n.)(-17+n.)(-10+n.)(-7+n.)2193639284471220096-1625672111159441216n.+208669970428152888

+12520867209735905

y.[n.]-(-28+n.)(-19+n.)(-16+n.)(-8+n.)450752022579939301890-418610006081815929939n.+113547189875676674449

-11467897264864991665

+461658093141561457

y.[1+n.]+14(-29+n.)(-21+n.)(-17+n.)(-10+n.)(-7+n.)2193639284471220096-1625672111159441216n.+208669970428152888

+12520867209735905

y.[2+n.]+(-28+n.)(-19+n.)(-16+n.)(-8+n.)450752022579939301890-418610006081815929939n.+113547189875676674449

-11467897264864991665

+461658093141561457

y.[3+n.]0,y.[1]1,y.[2]3,y.[3]5,y.[4]9,y.[5]12,y.[6]17,y.[7]22,y.[8]27,y.[9]33,y.[10]40,y.[11]48,y.[12]55,y.[13]61,y.[14]68,y.[15]74,y.[16]81,y.[17]87,y.[18]94,y.[19]101,y.[20]107,y.[21]114,y.[22]121,y.[23]128,y.[24]134,y.[25]141,y.[26]147,y.[27]154,y.[28]160,y.[29]167,y.[30]173,y.[31]179[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},40588-1063n.-18965

+5434

-344

+40628-35393n.+8938

-673

y.[n.]+-51712+44136n.-10733

+759

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

wm8525wm8525

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8525`wm8525`