You don't have to describe infinite (or very many) ever smaller layers at all times -- as with the fractal example, you can just render them when someone looks at them (which is almost always never below some point) and only at those areas and levels in which they look (make measurements) at a particular moment.
Besides, we assume a simulation that's uniformly behaving at all points. They designer of the simulation could very well hard-code the result of that experiment to be what it is.
As always, observer-dependent effects are actually information-dependent effects.
In this case, the Universe is simulated as a single entity. Since the behaviour of the Universe depends on its contents (i.e. we can gain information about the contents by observing the overall entity), this coarse-grained simulation is forced to sub-divide into smaller regions. The simulation keeps subdividing (some regions more than others) until it reaches a level where some hard-coded criterion is reached that further subdivision will have no effect on the outcome. For example, if an entire planet is getting swallowed by a star, it is not useful to simulate each atom of the planet; just treat the whole thing as one entity.
Unfortunately, the simulation has to spend a lot of resources simulating part of the Milky Way galaxy, because it contains a chaotic mechanism of "life", which may cause an observable effect on the Universe as a whole, e.g. by seeding galaxies with star-engulfing, self-replicating megastructures. In the region around Earth, the simulation was forced to sub-divide to a level we might call "classical mechanics", in order to calculate outcomes with enough precision.
Unfortunately, during the 20th Century, more subdivision has become necessary, as "life" has begun performing "experiments" with a precision beyond that of the "classical mechanics" level. These experiments act as amplifiers, turning very small effects (such as the discrete nature of space) into large ones (such as the publication of scientific papers, development of technology, colonisation of intergalactic space, etc.).
It turns out that the Universe is written in Haskell, and a "print" statement caused a thunk to be forced ;)
Anyone outside the simulation for starters. If you run a simulation and zoom to a certain area, you want to see it properly "rendered".
And people inside the simulation too, I guess. If they make measurements at some specific area and zoom level, you want them to get results for that level consistent with their model of the world -- not to have them see the "seams" of the simulation engine so to speak.
In addition to the other points, the thing simulating us need not run on our physics, or even resemble our physics. They may have infinite computational power. We don't, but that doesn't mean anything about them.
