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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},10,"LayeredCausalGraph"],VertexLabelsAutomatic,PerformanceGoal"Quality"]
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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},12,"CausalGraph"],VertexLabelsAutomatic]//LayeredGraphPlot
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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},12,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic]//LayeredGraphPlot
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NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},16,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot
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Table[NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},16,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot,5]
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Table[NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},20,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot,5]
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Table[NeighborhoodGraph[Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},5,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic],{1},2]//LayeredGraphPlot,5]
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Graph[WolframModel[{{x,y},{z,y}}{{x,z},{y,z},{w,z}},{{0,0},{0,0}},12,"CausalGraph","EventOrderingFunction""Random"],VertexLabelsAutomatic]//LayeredGraphPlot
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A Different Rule
A Different Rule
DrawFoliations
DrawFoliations
For generations, one must use the longest distance from the root
For generations, one must use the longest distance from the root
Shortest path foliation [ it is not a foliation ]
Shortest path foliation [ it is not a foliation ]
find other foliations
find other foliations
Note: this rendering “sorts in time”, because all arrows are pointing down.
In a valid causal foliation, the leaves cannot cross.....
In a valid causal foliation, the leaves cannot cross.....
Sequence of leaves in a causal foliation corresponds to a path in the multiway system (?)
Sequence of leaves in a causal foliation corresponds to a path in the multiway system (?)
In other words, every evolution history defines a set of spacelike hypersurfaces (?)
What is a valid foliation sequence?
What is a valid foliation sequence?
We could look at “valid updating orders” which have the property that they respect the partial ordering....
What happens in a trivial “diamond” graph
What happens in a trivial “diamond” graph
The partial order criterion is .....
Total orders
Total orders
Comparability graphs (?)
Comparability graphs (?)
Join spacelike separated nodes
Multiway Graph
Multiway Graph
Any particular causal graph contains some subset of these events
Any particular path defines a single sequence of events
Can a causal graph have closed timeline curves?
Can a causal graph have closed timeline curves?
(Maybe due to accidental isomorphism?)
Non-overlapping multiway graph
Non-overlapping multiway graph