Universe 8713 from The Wolfram Physics Project

60 steps

wm8713`wm8713`

signature

2₃→3₃

rule

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

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2,1},{3,4,5}}{{2,5,2},{1,6,2},{4,7,6}}},{{1,1,1},{1,1,1}},68,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},29-21n.+y.[n.]+y.[1+n.]+y.[2+n.]+y.[3+n.]0,y.[1]1,y.[2]3,y.[3]5,y.[4]9,y.[5]12,y.[6]17,y.[7]22,y.[8]27,y.[9]33,y.[10]37,y.[11]43,y.[12]48[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-44+11n.+3

+-28+19n.-3

y.[n.]+38-23n.+3

y.[1+n.]0,y.[1]2[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},



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

wm8713wm8713

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm8713`wm8713`