Universe 6891 from The Wolfram Physics Project

192 steps

wm6891`wm6891`

signature

2₃→3₃

rule

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

make editable copy
download notebook

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{4,1,4},{3,4,1},{2,4,5}}},{{1,1,1},{1,1,1}},500,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-1-y.[n.]+y.[1+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]5,y.[5]8,y.[6]11,y.[7]12,y.[8]13,y.[9]14,y.[10]15,y.[11]16,y.[12]17,y.[13]18,y.[14]19,y.[15]20,y.[16]21,y.[17]22,y.[18]23,y.[19]24,y.[20]25,y.[21]26,y.[22]28[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-1-y.[n.]+y.[1+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]6,y.[5]9,y.[6]12,y.[7]13,y.[8]14,y.[9]15,y.[10]16,y.[11]17,y.[12]18,y.[13]19,y.[14]20,y.[15]21,y.[16]22,y.[17]23,y.[18]24,y.[19]25,y.[20]26,y.[21]27,y.[22]29[t]

Result after

192

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},



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{4,1,4},{3,4,1},{2,4,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,1},{3,2,4}}{{4,1,4},{3,4,1},{2,4,5}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

