Universe 6821 from The Wolfram Physics Project

198 steps

wm6821`wm6821`

signature

2₃→3₃

rule

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

make editable copy
download notebook

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,1},{2,3,4}}{{5,3,5},{3,2,6},{3,4,6}}},{{1,1,1},{1,1,1}},500,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



	vertices
	edges

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

1+t

Result after

198

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

[{{{1,2,1},{2,3,4}}{{5,3,5},{3,2,6},{3,4,6}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2,1},{2,3,4}}{{5,3,5},{3,2,6},{3,4,6}}},{{1,1,1},{1,1,1}},<|"MaxEvents"198|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

