Cellular automata in physics and information quantity of a cell


I was taking a look at the 1994 PhD thesis of Mark Andrew Smith on Cellular Automata Methods in Mathematical Physics.  I could only find one subsequent paper by Smith, on polymer simulation in 1999 with B. Ostrovsky.  I assume he is no longer active.  The only other work I found was some apparently self-published work by Canadian engineers in 1999, Tom Ostoma and Mike Trushyk.  Like Smith they didn’t publish anything after 1999.  It doesn’t seem to be an actively pursued field.   The only reason I could find for this lack of pursuit was a comment on the Math Stack Exchange website by Willie Wong stating that

One of the reasons that it may be difficult to model Minkowski space based on cellular automata is that there are no “non-trivial” finite sub-groups of O(3,1), where non-trivial means that it doesn’t just reduce to just a finite sub group of O(3) via conjugation. So while cellular automata can be manifestly be homogeneous and isotropic (so admits a discrete O(3) symmetry), it becomes conceptually difficult to imagine some cellular automata capturing Lorentz symmetry.


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