So as a simple example one could imagine having a pattern laid out on a three-dimensional array with each successive vertical plane giving the evolution of some one-dimensional universal system from each of its successive possible initial conditions. And with this setup any computation, regardless of its sophistication, must appear somewhere in the pattern.

Occurrences of progressively longer blocks in the pattern generated by rule 30 starting from a single black cell. So far as I can tell, all possible blocks eventually appear, potentially letting the pattern serve as a kind of directory of all possible computations.