A Class of Models with the Potential to Represent Fundamental Physics
  1. Introduction
  2. Basic Form of Models
  3. Typical Behaviors
  4. Limiting Behavior and Emergent Geometry
  5. The Updating Process for String Substitution Systems
  6. The Updating Process in Our Models
  7. Equivalence and Computation in Our Models
  8. Potential Relation to Physics
  9. Additional Material
  10. References
  11. Index
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technical introduction Basic Form of Models

2.3 A Slightly Different Rule

Since order within each relation matters, the following is a different rule:

{{x, y}} -> {{z, y}, {y, x}}

This rule can be represented graphically as:

RulePlot[ResourceFunction[ "WolframModel"][{{x, y}} -> {{z, y}, {y, x}}], VertexLabels -> Automatic, "RulePartsAspectRatio" -> 0.25]

Like the previous rule, running this rule also gives a tree, but now with a somewhat different structure:

ResourceFunction[ "WolframModel"][{{{x, y}} -> {{z, y}, {y, x}}}, {{1, 2}}, 8]["StatesPlotsList", "MaxImageSize" -> 180]

With the other rendering from above, the last 3 steps here are:

Graph[Rule @@@ #, GraphLayout -> "LayeredDigraphEmbedding", VertexStyle -> ResourceFunction["WolframPhysicsProjectStyleData"]["SpatialGraph", "VertexStyle"], EdgeStyle -> ResourceFunction["WolframPhysicsProjectStyleData"]["SpatialGraph", "EdgeLineStyle"], AspectRatio -> 1/3] & /@ Take[ResourceFunction[ "WolframModel"][{{{x, y}} -> {{z, y}, {y, x}}}, {{1, 2}}, 8, "StatesList"], -3]
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