isotropy

I think you're right, but it's really isotropy in combination with independence of x and y.

Isn't the key point here about isotropy, similar to the velocities in the ideal gas?

Bostrom's postulates are exceedingly bad. His assumptions rely to much on the isotropy of properties of the one "real" existence and the simulated ones.

One other issue with voxel engines is isotropy, or rather, anisotropy.

With the usual cosmological assumptions of isotropy and homogeneity, then there's a big clock for everyone to use.

Of course, inflation is an untested theory, and there are competing ones which try to explain the apparent homogeneity and isotropy of the universe.

Originally it was a simple way to resolve outstanding issues of homogeneity and isotropy of the observable universe.

There are certainly places in the universe so far apart that light not only can't now, but could never, have travelled from one to the other; that is part of why the near-isotropy of background radiation is something that needs to be explained, I thought.

Global symmetries on the other hand are meaningful, for example spatial translation and rotations and time translations in Newtonian spacetime are associated with the isotropy and homogenity of space and time and also the related conservation of momentum, angular momentum, and energy.

Cellular automata violate continuity and isotropy, which means they're inconsistent with the continuous spatial formalism used in special relativity, general relativity, classical electrodynamics, and as far as I know, quantum electrodynamics.