Consider a Simple Mathematical Process

Consider a simple mathematical process, like an algorithm that generates the digits of Pi. Pi never stops, so in a way, the algorithm provides a window into an arrangement of information that's infinitely long.

Now look at a slightly more complicated process, such as Conway's Game of Life. Much like the Pi-computing algorithm, this is just another mathematical process, but the arrangement of information it describes is somehow richer: the game represents a 2D space evolving over time, with gliders, glider guns generating them, and so on.

What's interesting about both of these is that the "world" defined by the algorithms is in some way independent of actually running the simulation. Two people who calculate Pi will come up with the same answer. You can calculate 1000 digits of Pi and come back half an hour later, and calcluate another 1000 digits, and you'll have the same 2000 digits as someone who did 2000 at once.

Similarly, two people who run Conway's game (from the same starting conditions) will watch the same set of events unfold. Just as with Pi, they can stop the simulation, take a coffee break, and turn it on again, and the world inside continues completely unaware. You can rewind it, run it again, and it's all the same.

So in a way, simulations are a way of exploring a mathematical space. The existence of that space, in some ways at least, is independent of whether and when we explore it. The fact that a certain collision between 13 gliders happens on turn ten billion of a particular game seed is independently discoverable - it's already there, encoded in the rules, awaiting our discovery.

Now consider simulated worlds that are rich enough to develop artificial life, sophisticated enough to be self-aware. (By this, I mean that the simulated beings have an internal model of their world that includes a representation of themselves.) If you're a materialist, I think it's a short step to imagine that such beings could have an experience of themselves that's as rich and as convincing as ours is.

Nevertheless, we could pause that simulation, rewind it, run multiple copies, and none of this would affect the experience of the beings inside, because their experience is wholly encoded in the interplay of information that the simulation rules describe.

Much like the glider collision, or the 100th digit of Pi, their consciousness is already there. Running the simulation just allows us to experience it. Their world is real, to them. Even if we don't run the simulation.

Even if we don't .. invent it?

Now, if we discover that our world is based on a set of principles that could, in theory, be simulated, then what follows is that our world might not be 'real', either. Nobody's running it - nobody needs to!
Maybe somebody is running it, somewhere in another universe, but all that means is that they're exploring part if it. It doesn't mean that they're creating us, just that they know what we're up to (if they've run it this far).

Actually, this line of reasoning pretty much guarantees that an infinite multitude of different meta-worlds are exploring our universe through simulations, as well as all possible other universes, just exploring different parts of it.