P.S. As far as I know, computational complexity is the only physical quantity that doesn't obey conservation laws. So we're probably not in a simulation. If we were, it would probably be the other way around.
No, I don't think this is some sort of accidental emergent property. Likely the information complexity singularity is the whole point.
It’s hard for me to imagine the “information complexity” we’re inducing into the universe as significant compared to the total size of the state machine representing all the neutrinos and photons in the universe, let alone the other particles.
Also if the the universe is a simulation it makes sense the simulators would be working with snapshots since even if you have the computational capabilities to simulate an entire universe, you probably don’t want to waste whatever time/energy resources exist in the simulating universe, simulating the first few billion years till your simulated universe gets to the point you’re most interested in, be it changing parameters / picking the outcome of particular random outcome or just zooming in and studying what goes on in the randomness, or just looking at it like some kind of highly advanced virtual zen garden.
So I’m not entirely convinced that our electronic computation devices which operate by way of the movement of electrons or photonics devices operating by manipulating photons (and usually electrons too), represents our hypothetical simulators having to design or run a simulation of anything beyond what we call “normal operating behaviour of clumps of solid baryonic matter”. All the computers in the world, full of electrons and interconnected by fibre optic lasers, is unlikely to involve simulating more electrons, neutrinos, and other subatomic particle interactions than are necessary to simulate the earth’s inner and outer core and their electrodynamic (which are coupled to the solar electrodynamics) and thus simulate the production of the earths magnetic field.
Seeing how mindbogglingly huge the universe is, our insignificant planet is unlikely to be the most intensive object to simulate. For a Universe simulator it would be peanuts, less than peanuts, peanut crumbs that fell behind the pantry where you can't clean them.
Populating the world with interesting NPCs, is, however, a vastly more difficult problem than just scaling the same copy-pasted planets and stars across light years.
So no, the size of our universe is just a scale parameter. There's no evidence that it's more computationally complex out there than here, and computational complexity is the only interesting metric.
I understand your point, though, but even if it was true, keeping track of all the physics in the Universe's filler would demand more processing power than what is needed for our planet. The speed of light would be our rendering depth, and that's still an unthinkable amount of computing, copy-paste included.
If that were true then they wouldn't have built relativity into the model. (I think the speed of light exists to limit us to our sandbox.)