Universe 2678 from The Wolfram Physics Project

169 steps

wm2678`wm2678`

signature

2₃→3₃

rule

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

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Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},184,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

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

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

1+t

Result after

175

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



Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"175|>,"FinalStatePlot","EventOrderingFunction""Random"]

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,FinalStatePlot,EventOrderingFunctionRandom]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},<|"MaxEvents"175|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}



[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{OldestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelOldestEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{LeastOldEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastOldEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{LeastRecentEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastRecentEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{NewestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelNewestEdge],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{RuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelRuleOrdering],

[◼]	WolframModel

[{{{1,1,2},{3,4,5}}{{6,6,3},{6,5,1},{5,7,2}}},{{1,1,1},{1,1,1}},MaxEvents175,EventOrderingFunction{ReverseRuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelReverseRuleOrdering]

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

wm2678wm2678

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Other Evolution Orders

Graph Features of States

wm2678`wm2678`