This isn't quite answering your question, but you can do an exact model of fluid flow using finite state 2D cellular automata exact solutions to the Navier Stokes equation. This works in 2D and in hyper dimensional space but not in 3D space apparently. In 2D it is usually done on a hexagonal lattice which for some reason works much better. The rules are deterministic except that in some situations there is more than one outcome, if so one is chosen at random. See Lattice gas automaton
This gives an idea of the sort of thing. Just turned it up in a youtube video search.
And more examples here http://www.ift.uni.wroc.pl/~seba...
I think it's remarkable the way you get these flows that show no trace of the underlying grid hexagonal symmetries.
I don't know if Todd Rowland's examples are related or not.
Have just remembered, using similar methods, the same hexagonal lattice cellular automata, you get "lattice gas diffusion" which, staring with a circular patch, gives expanding circular diffusion patterns like this, pretty close to what you are asking for:
This gives an idea of the sort of thing. Just turned it up in a youtube video search.
And more examples here http://www.ift.uni.wroc.pl/~seba...
I think it's remarkable the way you get these flows that show no trace of the underlying grid hexagonal symmetries.
I don't know if Todd Rowland's examples are related or not.
Have just remembered, using similar methods, the same hexagonal lattice cellular automata, you get "lattice gas diffusion" which, staring with a circular patch, gives expanding circular diffusion patterns like this, pretty close to what you are asking for:
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Robert Walker
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