I'd implore everyone to spend a few rainy weekends trudging through Mandelbrot's 'The Fractal Geometry of Nature'[1] and Wolfram's 'A New Kind of Science'[2]. Both are rather terse, but I found both added a whole new depth of analogy in the way I see the Universe(s).
It's easy to be dismissive of Stephen Wolfram for his general asshat'ery and Benoit isn't around to champion his notions in the broader sense. But if we are to take reductivism to it's extreme, it's worth exploring emergent patterns with a bit more wonderment.
I don't know if one could call NKS terse, at over 1000 pages. It was a very enjoyable and mildly enlightening read, I'd recommend it, but I'd really like to see his theories fleshed out in a more formal way. It was a bit heavy on conjecture and speculation for me.
When discussing the idea that our universe is simulated, often the assumption is that it's an experiment by aliens or somesuch. But recently I've started to wonder if our parent universe is nearly identical to our own, and we are one of millions of virtual Earths used for political and economic predictions, because if (when) we could, that's exactly what we would do.
If true, this has an interesting implication - if our parent universe bothers to do it, it probably means they get useful information from it. That means that the recursion eventually terminates, that eventually in some great great grandchild universe they are able to produce the seed of the answer to whatever the original question was, rather than start another simulation.
My intuition is that the recursion shouldn't hurt getting useful results, even if the simulation was allowed to proceed past the point where such a simulation was developed (which they may not have), in a manner akin to the resolution of Zeno's Paradox. Though there's likely a bound on how many layers deep we can go, but my quantum information theory isn't what it used to be so I have to hand wave my conjectures.
That would apply to real-time simulations. But wouldn't every layer run successively slower? The inhabitants wouldn't notice how fast their simulation is running in the (grand)parent universe. So given infinite time the layering could be infinitely deep.
It could also simply be monitored for CPU usage, and have the process auto-terminate when spiked by recursive children. Creating our own Virtual Earth might then destroy the universe. :P
Another disturbing thought: if our universe were spun up or down like we do virtual machines, would we even notice?
I imagined I had given some thought to these subjects, but Permutation City did have new ideas. If you slow down a simulation to some ridiculous degree, the simulated beings don't notice. Even if you run the simulation backwards or in random order, they wouldn't notice. If you abruptly shut it down, they'll just continue finding the pattern somewhere.
If the recursion spawns an average of more than one child universe per parent universe, then it would spawn an infinite number of universes, and maybe this is still the first run which, to the disappointment of our unknown benefactors, will produce no useful information.
Which creates some disturbing ideas about our reality.