Wolfram Models & Analysis

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Wolfram Models & Analysis

Wolfram models are a general class of systems involving rewriting of hypergraphs. They are the fundamental models used as the basis for the

Wolfram Physics Project

.

Basic Model Implementation

□	WolframModel

— Wolfram model evolution, causal graphs, etc.

□	WolframModelEvolutionObject

— symbolic representation of Wolfram model evolution

□	WolframModelPlot

— visualization of Wolfram model hypergraphs

Multiway Evolution

□	MultiwaySystem

— multiway Wolfram model evolution

Rule Structure & Enumeration

□	WolframModelData

— data on Wolfram models in the

Registry of Notable Universes

□	CanonicalWolframModelRule

— find a canonical form for a Wolfram model

□	EnumerateWolframModelRules

— enumerate possible rules with a given signature

□	EnumerateRuleSignatures

— enumerate possible signatures with given total elements

□	RandomWolframModel

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□	ConnectedWolframModelQ

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□	CausalInvariantQ

Rule Display & Formatting

RulePlot

— give a visual representation of a Wolfram model rule

□	WolframModelRuleForm

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□	WolframModelSignatureForm

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□	WolframModelTraditionalForm

Hypergraph Generation

□	EnumerateHypergraphs

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□	RandomHypergraph

□	CanonicalHypergraph

— convert a hypergraph to canonical form

□	BranchialHypergraph

Hypergraph Properties

□	ConnectedHypergraphQ

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□	HypergraphAdjacencyMatrix

□	HypergraphNeighborhoods

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□	HypergraphNeighborhoodVolumes

Hypergraph Isomorphism

□	IsomorphicOrderedHypergraphQ

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□	FindOrderedHypergraphIsomorphism

□	IsomorphicHypergraphQ

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□	FindHypergraphIsomorphism

Conversion to Graphs

□	HypergraphToGraph

— convert to an ordinary graph by turning hyperedges into subgraphs

Low-Level Update Operations

SubsetReplace

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SubsetCases

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SubsetPosition

Graph Properties »

□	GraphNeighborhoodVolumes

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NeighborhoodGraph

FindShortestPath

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□	FindLongestPath

VertexCount

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GraphDiameter

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□	GraphAntipodes

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□	GraphMinors

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...

Graph Visualization »

GraphPlot

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GraphPlot3D

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LayeredGraphPlot

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□	LayeredGraphPlot3D

□	DistanceLayeredGraph

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Graph3D

□	GraphReconstructedSurface

— render a graph in 3D with an approximate surface

□	GraphFunctionPlot

— visualize a function on a graph

Ordered Trivalent Graph Models

□	OrderedGraphModelPlot

— visualize ordered trivalent graphs

Graph Generation

□	TorusGraph

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□	GeneralizedGridGraph

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□	HexagonalGridGraph

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□	HexagonalTorusGraph

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□	BuckyballGraph

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□	GeodesicSphereGraph

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□	RegularHyperbolicTilingGraph

MeshConnectivityGraph

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□	GraphicsMetricGraph

Causal Graph Generation

□	CurvedSpacetimeRegionSprinkling

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□	CurvedSpacetimeSprinkling

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□	FlatSpacetimeSprinkling

□	CausalConnectionGraph

— summarize future overlaps in a causal graph

Spatial Graph Generation

□	ExtrinsicCurvedManifoldToGraph

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□	IntrinsicCurvedManifoldToGraph

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FlatManifoldToGraph

RelatedGuides

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Graph Theory

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Graph Visualization

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Wolfram Physics Project Functions

RelatedLinks

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Wolfram Physics Project Home Page

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Hands-On Introduction to the Wolfram Physics Project

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Wolfram Physics Project: Technical Introduction