Asklemmy

I took it from an information theory perspective:

1. Turing machines can compute anything defined as an algorithm, and cannot compute anything that cannot be defined as an algorithm. This is why, for example, computers can't generate random numbers (only deterministic streams of pseudorandom numbers using some starting seed). Also all Turing machines are equivalent -- they can all run the same set of algorithms given sufficient memory and will produce the same result.
2. By Bell's inequality, we know that certain events (I use quantum-tunneling) are non-deterministic and cannot be predicted by an algorithm (at better than chance, given infinite computing power, infinite time, and perfect knowledge of the system). Note though I'm an amateur quantum mechanic at best :D
3. Therefore if the universe is a simulation running on a Turing-machine, they would have to either halt, use pseudorandom numbers (which I can detect with finite but large CPU power and finite but large time), or sample their own random numbers from a local entropy source.

This way I try to minimize assumptions about physical laws in the Universe 'upstairs'. One interesting property of this is that if the universe upstairs is also simulated, then if it samples local entropy it just passes the problem upward :D

I do work with the assumption that a Turing machine runs any simulation, Matrix-style. Not some underlying physical process that just so happens to simulate a Universe, and also put entropy in all the right places whenever I look.

This is all just for amusement though. If the Universe was really running on a Turing machine, we'd see way more ads (drink your ovaltine encoded in pi?). Also the current design is really suboptimal what with all the entropy. No way it would run for 13-point-whatever billion years. I refuse to believe that our hypothetical extradimensional programmers are simultaneously that smart and that dumb :P