>any cellular automaton that has something like 3-dimensional rotational symmetry
Kind of cheating : but a differentiable 3d field of real numbers following a local Hamiltonian evolution is a kind of cellular automaton : it has a lot of states 2^32 and local evolution rules are the mathematical ones for differentiable calculus so they encode the rotational symmetry, you can approximate to any levels of desired precision.
Kind of cheating : but a differentiable 3d field of real numbers following a local Hamiltonian evolution is a kind of cellular automaton : it has a lot of states 2^32 and local evolution rules are the mathematical ones for differentiable calculus so they encode the rotational symmetry, you can approximate to any levels of desired precision.