There are several papers that propose that the universe itself is analogous to a cellular automata. Obviously, these papers assume that the universe is computable.
But is it there any cosmological cellular automata models that would allow uncomputable laws/processes/functions/numbers/things...etc to exist in that universe? For example, cellular automata universes where there would be truly black hole-singularities (which are uncomputable)?
Maybe Konrad Zuse's cellular automata could do the job?
Or maybe some variation of Conway's game of life? https://en.m.wikipedia.org/wiki/Conway%27s_Game_of_Life
Or maybe we could build one using 't Hooft's cellular automata frameworks