Universe 1869 from The Wolfram Physics Project

8 steps

wm1869`wm1869`

signature

2₂→5₂

rule

{{{1, 2}, {1, 3}} -> {{1, 4}, {1, 5}, {4, 2}, {5, 2}, {3, 4}}}

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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

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Event-by-event evolution:

[◼]	WolframModel

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

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

Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{1,3}}{{1,4},{1,5},{4,2},{5,2},{3,4}}},{{1,1},{1,1}},15,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},1+2y.[n.]-y.[1+n.]+2y.[2+n.]-3y.[3+n.]+y.[4+n.]0,y.[1]1,y.[2]3,y.[3]5,y.[4]9,y.[5]15[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},1+2y.[n.]-y.[1+n.]+2y.[2+n.]-3y.[3+n.]+y.[4+n.]0,y.[1]2,y.[2]5,y.[3]8,y.[4]14,y.[5]23[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"],

ListIcon

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Final State Properties

Hypergraph adjacency matrix:

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

WolframModel[

]

["FinalState"],

ListIcon

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Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],

ListIcon

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Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,

ListIcon

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Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],

ListIcon

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Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4

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

Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

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

ListIcon



Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],

ListIcon

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Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],

ListIcon



Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},

ListIcon

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Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,2},{1,3}}{{1,4},{1,5},{4,2},{5,2},{3,4}}},{{1,1},{1,1}},<|"MaxEvents"66|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{1,3}}{{1,4},{1,5},{4,2},{5,2},{3,4}}},{{1,1},{1,1}},<|"MaxEvents"66|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

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