Universe 3841 from The Wolfram Physics Project

99 steps

wm3841`wm3841`

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2₃→4₃

rule

{{{1, 1, 2}, {3, 4, 5}} -> {{6, 6, 7}, {1, 6, 4}, {8, 9, 6}, {10, 3, 4}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},6,"StatesPlotsList"]





Event-by-event evolution:

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"6|>,"EventsStatesPlotsList"]





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},113,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,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

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"99|>,"FinalStatePlot","EventOrderingFunction""Random"]

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,FinalStatePlot,EventOrderingFunctionRandom]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},<|"MaxEvents"99|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}



[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{OldestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelOldestEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{LeastOldEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastOldEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{LeastRecentEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastRecentEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{NewestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelNewestEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{RuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelRuleOrdering],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,7},{1,6,4},{8,9,6},{10,3,4}}},{{1,1,1},{1,1,1}},MaxEvents99,EventOrderingFunction{ReverseRuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelReverseRuleOrdering]

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

wm3841wm3841

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Other Evolution Orders

Graph Features of States

wm3841`wm3841`