Universe 4768 from The Wolfram Physics Project

6 steps

wm4768`wm4768`

signature

1₂→3₂

rule

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,1}}{{2,2},{2,2},{1,2}}},{{1,1}},14,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

-1+t

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

-1+

Result after

generations:

WolframModel[

]

["FinalStatePlot"]

WolframPhysics`Build`Private`evolution$7933917[FinalStatePlot]

Causal Graph

Causal graph:

WolframModel[

]

"CausalGraph",

Rule[

]



WolframPhysics`Build`Private`evolution$7933917[CausalGraph,GraphLayoutSpringElectricalEmbedding]

Layered rendering:

WolframModel[

]

["LayeredCausalGraph"]

WolframPhysics`Build`Private`evolution$7933917[LayeredCausalGraph]

Causal graph distance matrix:

MatrixPlotTransposeGraphDistanceMatrix

WolframModel[

]

["CausalGraph"],



MatrixPlot[Transpose[GraphDistanceMatrix[WolframPhysics`Build`Private`evolution$7933917[CausalGraph]]],{ImageSizeSmall,FrameTicksNone}]

Final State Properties

Hypergraph adjacency matrix:

MatrixPlotAdjacencyMatrix@CatenateMapUndirectedEdge@@@Subsets[#,{2}]&,

WolframModel[

]

["FinalState"],



MatrixPlot[AdjacencyMatrix[Catenate[WolframPhysics`Build`Private`evolution$7933917[Subsets[FinalState,UndirectedEdge[2]]]]],{ImageSizeSmall,FrameTicksNone}]

Vertex degree distribution:

HistogramValuesCountsCatenateUnion/@

WolframModel[

]

["FinalState"],



Histogram[Values[Counts[Catenate[WolframPhysics`Build`Private`evolution$7933917[Union[FinalState]]]]],{ImageSizeSmall,FrameTicksNone}]

Neighborhood volumes (ignoring directedness of connections):

volumes=

[◼]	RaggedMeanAround

Values

[◼]	HypergraphNeighborhoodVolumes



WolframModel[

]

["FinalState"],All,Automatic;

ListLogLogPlotvolumes,



ListLogLogPlot

[◼]	RaggedMeanAround

Values

[◼]	GraphNeighborhoodVolumes

UndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],All,Automatic,{ImageSizeSmall}

Effective dimension versus radius:

ListLinePlot

[◼]	LogDifferences

[volumes],



ListLinePlot

[◼]	LogDifferences



[◼]	RaggedMeanAround

Values

[◼]	GraphNeighborhoodVolumes

UndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],All,Automatic,{ImageSizeSmall}

Successive neighborhood balls around a random vertex:

[◼]	HypergraphNeighborhoods



WolframModel[

]

["FinalState"],4

HighlightGraphNeighborhoodGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],WolframPhysics`Build`Private`evolution$7933917[FinalState],1,WolframPhysics`Build`Private`evolution$7933917[FinalState],HighlightGraphNeighborhoodGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],WolframPhysics`Build`Private`evolution$7933917[FinalState],2,WolframPhysics`Build`Private`evolution$7933917[FinalState],HighlightGraphNeighborhoodGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],WolframPhysics`Build`Private`evolution$7933917[FinalState],3,WolframPhysics`Build`Private`evolution$7933917[FinalState],HighlightGraphNeighborhoodGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],WolframPhysics`Build`Private`evolution$7933917[FinalState],4,WolframPhysics`Build`Private`evolution$7933917[FinalState]

Distance matrix:

distanceMatrix=GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

MatrixPlotExp[-(distanceMatrix/.0None)],



MatrixPlot

-GraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]]



,{ImageSizeSmall,FrameTicksNone}

Distribution of distances in the graph:

HistogramFlatten[distanceMatrix],



HistogramGraphDistanceMatrixUndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],{ImageSizeSmall}

Spreading of Effects

Causal graph adjacency matrix:

MatrixPlotAdjacencyMatrix

WolframModel[

]

["CausalGraph"],



MatrixPlot[AdjacencyMatrix[WolframPhysics`Build`Private`evolution$7933917[CausalGraph]],{ImageSizeSmall}]

Neighborhood volumes in causal graph:

ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes



WolframModel[

]

["CausalGraph"],{1},



ListLogLogPlotValues

[◼]	GraphNeighborhoodVolumes

[WolframPhysics`Build`Private`evolution$7933917[CausalGraph],{1}],{ImageSizeSmall}

Other Evolution Orders

Random evolutions:

[◼]	WolframModel

[{{{1,1}}{{2,2},{2,2},{1,2}}},{{1,1}},<|"MaxEvents"63|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,1}}{{2,2},{2,2},{1,2}}},{{1,1}},<|"MaxEvents"63|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}





Graph Features of States

graph=

[◼]	HypergraphToGraph



WolframModel[

]

["FinalState"];

HistogramClosenessCentrality[graph],



HistogramClosenessCentrality

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]],{ImageSizeSmall}

Cycle properties:

EdgeCycleMatrix[UndirectedGraph[graph]]//MatrixPlot

MatrixPlotEdgeCycleMatrixUndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]]

Histogram[Length/@FindFundamentalCycles[UndirectedGraph[graph]]]

Histogram[FindFundamentalCycles[1]]

FindSpanningTree[UndirectedGraph[graph]]

FindSpanningTreeUndirectedGraph

[◼]	HypergraphToGraph

[WolframPhysics`Build`Private`evolution$7933917[FinalState]]

‹ Registry of Notable Universe Models

wm4768wm4768

Basic Evolution

Causal Graph

Final State Properties

Spreading of Effects

Other Evolution Orders

Graph Features of States

wm4768`wm4768`