Universe 3818 from The Wolfram Physics Project

10 steps

wm3818`wm3818`

signature

2₂→4₂

rule

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

make editable copy
download notebook

Basic Evolution

Basic evolution:

[◼]	WolframModel

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





Event-by-event evolution:

[◼]	WolframModel

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





Vertex and edge counts:

{vertexCountList,edgeCountList}=

[◼]	WolframModel

[{{{1,2},{2,3}}{{2,3},{2,4},{3,4},{1,4}}},{{1,1},{1,1}},23,{"VertexCountList","EdgeCountList"}];

ListLogPlot{vertexCountList,edgeCountList},

SequenceIcon



	vertices
	edges

Symbolic expression for vertex count:

FindSequenceFunction[vertexCountList,t]

DifferenceRootFunction{y.,n.},-3-y.[n.]-3y.[1+n.]-2y.[4+n.]+y.[7+n.]0,y.[1]1,y.[2]2,y.[3]3,y.[4]4,y.[5]7,y.[6]11,y.[7]15[t]

Symbolic expression for edge count:

FindSequenceFunction[edgeCountList,t]

DifferenceRootFunction{y.,n.},-6-y.[n.]-3y.[1+n.]-2y.[4+n.]+y.[7+n.]0,y.[1]2,y.[2]4,y.[3]6,y.[4]8,y.[5]14,y.[6]22,y.[7]30[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"],

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},{2,3}}{{2,3},{2,4},{3,4},{1,4}}},{{1,1},{1,1}},<|"MaxEvents"75|>,"FinalStatePlot","EventOrderingFunction""Random"]

Different deterministic evolution orders:

[◼]	WolframModel

[{{{1,2},{2,3}}{{2,3},{2,4},{3,4},{1,4}}},{{1,1},{1,1}},<|"MaxEvents"75|>,"EventOrderingFunction"{#,"LeastRecentEdge","RuleOrdering","RuleIndex"}]["FinalStatePlot",PlotLabel#]&/@{"OldestEdge","LeastOldEdge","LeastRecentEdge","NewestEdge","RuleOrdering","ReverseRuleOrdering"}

