Universe 99198 from The Wolfram Physics Project

Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,2,3,4},{5,6,7,8},{2,6},{6,2}}{{9,4,10,11},{12,8,13,14},{15,16,17,3},{18,19,20,7},{10,16},{16,10},{11,14},{14,11},{13,19},{19,13},{17,20},{20,17}}},{{1,1,1,1},{1,1,1,1},{1,1},{1,1}},1,"StatesPlotsList"]

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,

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Event-by-event evolution:

[◼]	WolframModel

[{{{1,2,3,4},{5,6,7,8},{2,6},{6,2}}{{9,4,10,11},{12,8,13,14},{15,16,17,3},{18,19,20,7},{10,16},{16,10},{11,14},{14,11},{13,19},{19,13},{17,20},{20,17}}},{{1,1,1,1},{1,1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"EventsStatesPlotsList"]

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,

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Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,3,4},{5,6,7,8},{2,6},{6,2}}{{9,4,10,11},{12,8,13,14},{15,16,17,3},{18,19,20,7},{10,16},{16,10},{11,14},{14,11},{13,19},{19,13},{17,20},{20,17}}},{{1,1,1,1},{1,1,1,1},{1,1},{1,1}},1,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



vertices

Result after

1

generations:

WolframModel[

]

["FinalStatePlot"]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]

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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],

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Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4

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,

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Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

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



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

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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

[{{{1,2,3,4},{5,6,7,8},{2,6},{6,2}}{{9,4,10,11},{12,8,13,14},{15,16,17,3},{18,19,20,7},{10,16},{16,10},{11,14},{14,11},{13,19},{19,13},{17,20},{20,17}}},{{1,1,1,1},{1,1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,3,4},{5,6,7,8},{2,6},{6,2}}{{9,4,10,11},{12,8,13,14},{15,16,17,3},{18,19,20,7},{10,16},{16,10},{11,14},{14,11},{13,19},{19,13},{17,20},{20,17}}},{{1,1,1,1},{1,1,1,1},{1,1},{1,1}},<|"MaxEvents"1|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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