Universe 8678 from The Wolfram Physics Project

1 steps

wm8678`wm8678`

signature

2₂1₃→3₂2₃

rule

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

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,3},{4,4},{5,3}}{{3,2,4},{3,4,5},{1,5},{2,6},{7,8}}},{{1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"EventsStatesPlotsList"]





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

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

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



vertices

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"],

ListIcon



Final State Properties

Hypergraph adjacency matrix:

MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,

WolframModel[

]

["FinalState"],

ListIcon



Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],

ListIcon



Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,

ListIcon



Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],

ListIcon



Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4





Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

MatrixPlotExp[-(distanceMatrix/.0None)],

ListIcon



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

ListIcon



Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],

ListIcon



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},

ListIcon



Graph Features of States

graph=

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

HistogramClosenessCentrality[graph],

ListIcon



Cycle properties:

EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlot

Histogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]

FindSpanningTree[UndirectedGraph[graph]]

‹ Registry of Notable Universe Models

wm8678wm8678

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8678`wm8678`