Underlying Rule

(Actual rule for our universe is not known)
RulePlot[WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}]]
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Main Graphic

Initial condition ->

[[[ show in 3D ]]]
I don’t know how to deal with gaps around vertices and overlapping vertex plots. Maybe, Jonathan can help.
MultiwaySystem["WolframModel"{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{{0,0},{0,0}}},3,"EvolutionCausalGraph",VertexSize3,AspectRatio1]
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PATH TO HIGHLIGHT:
[[[ causal connection ]]]
[[[ updating event ]]]
[[[ branching of states ]]]
[[[ merging of states ]]]
[[[[ spacelike direction ]]]]
[[[ timelike direction ]]]
[[[ branchlike direction ]]]

Branch of evolution ->

Branch points to this
These are consistent with the branch shown above.
WolframModel[{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}},{{1,1},{1,1}},4,"EventsStatesPlotsList","EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]
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This follows the same branch further.
WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},8,"StatesPlotsList","EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]
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Spatial hypergraph

[[ spacelike directions : rosette of arrows ( 3 arrows, one slightly shorter ) ]]
Still on the same branch (much further)
WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},12,"FinalStatePlot","EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]
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Two generations more:
WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},14,"FinalStatePlot","EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]
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Even more two generations:
WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},16,"FinalStatePlot","EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]
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Causal graph ->

[[[ within: spacelike hypersurface ]]]]
[[[ energy is spacelike flux of causal edges ]]]
[[ In this plot: dotted line horizontal line :
direction ]]
[[ arrow down : timelike direction ]]
WolframModel[{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{0,0},{0,0}},7,"EventOrderingFunction"{"LeastRecentEdge","ReverseRuleOrdering"}]["LayeredCausalGraph",AspectRatio1]
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Branchlike hypersurface ->

[[ branchlike directions ]] ( lots ‘o arrows )
<< [[[ on an edge: i ℏ τ ]]] ?? >>
MultiwaySystem["WolframModel"{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{{0,0},{0,0}}},3,"BranchialGraph",VertexSize1.2]
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Callouts

Annotation

Multiway Causal Graph

MultiwaySystem["WolframModel"{{{x,y},{x,z}}{{x,z},{x,w},{y,w},{z,w}}},{{{0,0},{0,0}}},3,"CausalGraph",VertexSize3,AspectRatio1]
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