Can't find any proof of that claim. So far it seems more likely that all physical systems are computable. Although you may need infinite time to achieve perfect accuracy when computing them in a simulation, but matematically that's still computable.

Computability makes no assumption on the geometry, only on the rules the system follows.

Hm, I was not aware of that.

What about for, uh...

It occurs to me that I'm not exactly sure what a chaotic function of continuous real variables is.

Is it like, one where iterating it gives chaotic results, or?

What if, instead of variables over the reals, using variables over the computable reals?

There's also no proof (or even evidence) that the universe is not discrete.