Universe 8456 from The Wolfram Physics Project

89 steps

wm8456`wm8456`

signature

2₂→3₂

rule

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

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1},{2,3}}{{4,4},{4,2},{2,3}}},{{1,1},{1,1}},102,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},4+(3-n.)y.[n.]+(-4+n.)y.[1+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]6[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},5+(3-n.)y.[n.]+(-4+n.)y.[1+n.]0,y.[1]2,y.[2]3,y.[3]4,y.[4]5,y.[5]7[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

wm8456wm8456

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8456`wm8456`