You're talking about Plato's cave shadows and Korzybski's territorial map as mental simulations of the physical world? They might be called simulations, but in that sense, human perception is a very loose simulation of reality, only good enough for us to successfully inhabit our place in the universe and sometimes not even that (in the case of asylum inmates). The mind's simulation of reality is not a simulation in a scientifically practical sense.
I'm not willing to call the universe a simulation of itself. I agree with the idea of using the universe to simulate itself, though. Computer simulations are limited by accuracy and time, but if you assume arbitrary amounts of time, and if you don't need perfect accuracy (or laws of physics dictate safe time/space steps for the simulation), you can theoretically simulate arbitrarily complex physics for a brief amount of time. Sorry for stating the obvious with that, but I'd like to contrast the typical "computer simulation" idea with the following: I consider physics experiments to be attempts at using the universe (a small part of it) to simulate other parts of the universe. Computer simulations pale in comparison.
I got lost on this part of your comment: "So my experience is a simulation, but what it is being simulated by is, in fact, my experience. Thus: A simulation of itself."
Entertaining mental maps as simulations, for the sake of argument, I agree with the first part: mental (inner) experience is a simulation of sorts of the outer world. I don't understand the second half of your first sentence. The "what" that is providing your perception (inner experience) is your brain, right? I don't understand how you're making the connection that the brain is your experience. That seems like a lazy use of the word "is", and with a narrower replacement, the equivalence would not hold and you would not be able to claim "the universe simulates itself".