Whats wrong with a pseudo-random number generator? You start the universe with 1 million random bits and then just iterate your function on them. How would we detect repetition at the 2^1 mil level? Maybe the universe would repeat itself after a while, but how would we know?

Superdeterminism also plays nicely with the simulation hypothesis. You seed the virtual machine with some randomness and the physical laws and then you run the simulation.