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GridGraph[{30,30}]
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ResourceFunction["FlatManifoldToGraph"][10,1,100]["SpatialGraph"]
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ResourceFunction["FlatManifoldToGraph"][10,1,300]["SpatialGraph"]
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ResourceFunction["FlatManifoldToGraph"][10,.5,300]["SpatialGraph"]
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“Dimension diffusion”
“Dimension diffusion”
Fix the number of elements, and the number of connections....
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ResourceFunction["WolframModel"][{{x,y},{y,z},{z,w},{w,v}}{{y,u},{u,v},{w,x},{x,u}},List@@@EdgeList@GridGraph[{10,10}],5,"StatesPlotsList"]
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ResourceFunction["WolframModel"][{{x,y},{y,z},{z,w},{w,v}}{{y,u},{u,v},{w,x},{x,u}},List@@@EdgeList@GridGraph[{5,5,5}],5,"StatesPlotsList"]
Given a graph, randomly delete edges; what does this do to the dimension?
Given a graph, randomly delete edges; what does this do to the dimension?
Is there a percolation-like phenomenon, e.g. a dimension phase transition?
Is there a percolation-like phenomenon, e.g. a dimension phase transition?
What do random changes to a graph do to dimension?
What do random changes to a graph do to dimension?
Might not go down, if you are effectively preferentially deleting from close to the point you’re starting from
Continuum theory of dimension change: what attributes of a graph does it depend on?
When you delete edges in a ball, the fraction of the periphery that is removed is much less than the fraction of the center that’s removed: i.e. there will be a higher dimension, not lower....
Probably the jumps are due to pieces of the universe breaking off.......
Looking out a small distance:
For the above radii, the “inside” is too small to get zapped ... so there is no increase in dimension....
Torus graph
Torus graph
There is no boundary .... but it never reaches its full “dimension potential” ;; there are lots of paths going around the universe