Are you talking about the type writing monkey?
Don't think that's how it works...
I think you mean infinite realities?
Space is infinite, the universe is not.
That's not what infinite space implies.
So... We know that there are supermassive black holes, right? We know that black holes can swallow everything, even other black holes, causing a merger, and a bigger black holes... Eventually, it all gets pulled back in, into one hyper-dense "singularity" in pretty much the same composition, then explodes out like in the "big bang". It has all already happened, and it will happen countless more times... This... Cyclic Hell.
That would be a parallel universe...a mirror universe is more likely, where you could view yourself living your life watching movies