Universe 9152 from The Wolfram Physics Project

12 steps

wm9152`wm9152`

signature

2₂→3₂

rule

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

make editable copy
download notebook

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{2,3}}{{1,3},{3,4},{4,2}}},{{1,1},{1,1}},25,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-2-3y.[n.]+y.[3+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]5,y.[5]7,y.[6]11,y.[7]16,y.[8]23,y.[9]34[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-3y.[n.]+y.[3+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]6,y.[5]8,y.[6]12,y.[7]17,y.[8]24,y.[9]35[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},



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2},{2,3}}{{1,3},{3,4},{4,2}}},{{1,1},{1,1}},<|"MaxEvents"151|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{2,3}}{{1,3},{3,4},{4,2}}},{{1,1},{1,1}},<|"MaxEvents"151|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

