Take Wolfram's 1-dimensional cellular automata... some of them have infinite complexity, and of course you can "run" them for infinite time, and the "current" state is constantly expanding (like the Universe). So let's define "something feasible" as some specific finite bit pattern on the 1-dimensional line of an arbitrary current state. Is that "feasible" bit pattern guaranteed to appear anywhere in the automaton's present or future? I believe, and if I understand correctly, so does Wolfram, that for any reasonably complex "feasible pattern" the answer is no; even though the automaton produces infinitely many states, it is not guaranteed to explore all conceivable states.

In other words, in a given Universe (which has a specific set of rules that govern its evolution in time) even though there are infinitely many possible states, not all conceivable states are a possible result of that evolution.