Universe 3111 from The Wolfram Physics Project

34 steps

wm3111`wm3111`

signature

3₂→5₂

rule

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

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1},{2,1},{3,3}}{{2,2},{2,1},{4,2},{4,1},{3,3}}},{{1,1},{1,1},{1,1}},32,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

1+2t

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

wm3111wm3111

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Graph Features of States

wm3111`wm3111`