The Game of Life on an infinite grid, starting from a uniformly random pattern (i.e. each cell is either alive or dead with probability 1/2), gives you a whole

The Game of Life on an infinite grid, starting from a uniformly random pattern (i.e. each cell is either alive or dead with probability 1/2), gives you a whole multiverse which is governed by rules different from our own which probably contains intelligent life somewhere within it. Is that what you are looking for, or are you instead asking for an alternate universe where the rules of mathematics itself (or possibly even logic) are different? There are mathematical models of alternate universes where math and logic don't work, in the sense that a person living in those universes would easily prove that 1 = 0 from the Peano axioms (and would presumably give up on either the Peano axioms or first-order logic as a result). These mathematical models are uncomputable (so we can't actually simulate one like we can with the Game of Life), but they can be defined unambiguously and could even be simulated if we had access to a halting oracle. But even these alternate universes where math doesn't work are still built out of math - it's hard to even imagine a model of something which isn't built out of math.