Universe 6793 from The Wolfram Physics Project

50 steps

wm6793`wm6793`

signature

2₃→4₃

rule

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

make editable copy
download notebook

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},62,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-29122275(-4+n.)(-3+n.)-(-16+n.)(-7+n.)(-76047+38149n.)y.[n.]+(-6+n.)1984879-1129289n.+64504

y.[1+n.]+-1035630+160206n.+9384

y.[2+n.]+26355(-4+n.)(-3+n.)y.[3+n.]+26355(-4+n.)(-3+n.)y.[4+n.]+26355(-4+n.)(-3+n.)y.[5+n.]+26355(-4+n.)(-3+n.)y.[6+n.]+26355(-4+n.)(-3+n.)y.[7+n.]+26355(-4+n.)(-3+n.)y.[8+n.]+-8201004+5837284n.-927119

+38149

y.[9+n.]+12225534-8945098n.+1542668

-64504

y.[10+n.]+1351890-344691n.+16971

y.[11+n.]0,y.[1]1,y.[2]5,y.[3]9,y.[4]15,y.[5]21,y.[6]28,y.[7]35,y.[8]40,y.[9]47,y.[10]54,y.[11]59,y.[12]66,y.[13]72,y.[14]78,y.[15]85,y.[16]91,y.[17]97,y.[18]104,y.[19]111,y.[20]116,y.[21]123,y.[22]129,y.[23]135,y.[24]142,y.[25]148,y.[26]153[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},6+(2-n.)y.[n.]+(-3+n.)y.[1+n.]0,y.[1]2,y.[2]4,y.[3]6,y.[4]10[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

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},<|"MaxEvents"98|>,"FinalStatePlot","EventOrderingFunction""Random"]

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,FinalStatePlot,EventOrderingFunctionRandom]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},<|"MaxEvents"98|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}



[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,EventOrderingFunction{OldestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelOldestEdge],

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,EventOrderingFunction{LeastOldEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastOldEdge],

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,EventOrderingFunction{LeastRecentEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelLeastRecentEdge],

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,EventOrderingFunction{NewestEdge,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelNewestEdge],

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,EventOrderingFunction{RuleOrdering,LeastRecentEdge,RuleOrdering,RuleIndex}][FinalStatePlot,PlotLabelRuleOrdering],

[◼]	WolframModel

[{{{1,2,2},{3,4,5}}{{2,6,6},{6,5,1},{1,7,8},{9,5,8}}},{{1,1,1},{1,1,1}},MaxEvents98,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

wm6793wm6793

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Other Evolution Orders

Graph Features of States

wm6793`wm6793`