[mietek]

> Personally, I am curious if there is any cellular automaton that has something like 3-dimensional rotational symmetry.

Have you seen the Miller-Fredkin paper on circular motion of strings in cellular automata?

https://arxiv.org/abs/1206.2060

[lacker]

I haven't seen that, but the fact that you posted this interesting link makes me glad I commented! Will check it out