Any universe that contains AIXI would be too complex to be modeled by AIXI. AIXI requires finding programs that reproduce it's inputs exactly. But you could get past this constraint by looking for programs that predict the data, rather than recreating it exactly.

You could make it's environment an actual computer. Something like Core Wars. That makes creating and simulating it a lot simpler.

This would be an interesting experiment to do, although I predict AIXI would just kill itself fairly quickly.