Computer guy likes the idea that physics is a computer. What a surprise.

Like literally nothing distinguishes this idea in boldness from other ideas except that its not the current mainstream view. Also, no experimental verification.

If spacetime had a discrete character at scales like the inverse of the universe scale we would see dispersion of light as it traveled cosmological distances and we do not observe this. It is technically possible that the discreteness scale is much, much smaller than the inverse universe scale, of course, but at this point it seems pointless to me to entertain discrete models without some other compelling experimental means of determining its presence. I believe folks are trying to figure this out, but at present, my money remains on spacetime being continuous. I don't know shit, but I expect good quantum gravity theories will need to be scale free.

In general I think this CA stuff is much less deep than it seems to be. You can, of course, approximate continuous differential equations with discrete difference equations, which is, fundamentally, what all this boils down to, in the end. It isn't surprising that with appropriate rules one can reproduce smooth mechanics at scales way above the discreteness scale.