Could it be that some place out there in the computational universe, we might find our physical universe? - Stephen Wolfram

That's... the big discovery of this principle of computational equivalence of mine. ...This is something which is kind of a follow-on to Gödel's theorem, to Turing's work on the ... that there is this fundamental limitation built into science, this idea of computational irreducibility that says that even though you may know the rules by which something operates, that does not mean that you can readily... be smarter that it and jump ahead and figure out what it's going to do.

Problem 9. What is the correspondence between cellular automata and continuous systems?
Cellular automatat are discrete in several respects. First, they consist of a discrete spatial lattice of sites. Second, they evolve in discrete steps. And finally, each site has only a finite discrete set of possible values.
The first two forms of discreteness are addressed in the numerical analysis of approximate solutions to, say, differential equations. ...
The third form of discreteness in cellular automata is not so familiar from numerical analysis. It is an extreme form of round-off, in which each "number" can have only a few possible values (rather than the usual 2¹⁶ or 2³²).

I thought... I had a pretty good idea for what the structure of this... theory that's underneath space and time and so on might be like. ...I thought, "Gosh, in my lifetime... we might be able to figure out what happens in the first 10^-100 seconds of the universe. ...It's pretty far from anything that we can see today and it would be ...hard to test for what's right ...To my huge surprise, although it should have been obvious, ...we managed to get unbelievably much further than that. ...It turns out that even though there's this ...bed of computational irreducibility that ...all these simple rules run into, ...there are ...certain pieces of computational reducibility that ...generically occur for large classes of these rules, and... the big pieces of computational reducibility are ...the pillars of 20th century physics. That's the amazing thing, that general relativity and quantum field theory... turn out to be precisely the stuff you can say. There's a lot you can't say... at this... irreducible level where you.. don't... know what's going to happen. You have to run it [and] you can't run it within our universe... The things you can say turn out to be, very beautifully, exactly the structure that was found in 20th century physics...