> It could also use relative coordinates - each particle in the simulation is defined based on the angle and distance to the nearest other particle. (Where angle is relative to the spin axis of the particle - no global angle.)
Are you sure? IMO, these coordinates will not be infinitely precise, lest they require infinite memory. Consequently, you would find that the space of possible angles and distances is in fact discrete, as it were defined by a lattice. The structure of the coordinate system is implicit in this case.
> Consequently, you would find that the space of possible angles and distances is in fact discrete,
And it is! Angular momentum is quantized. Angle itself probably isn't, but the motion is, and everything is always moving. That's one of the most interesting parts of this theory - as best as we can tell everything is actually quantized, so you can definitely have discrete values for the universe simulation.
> The structure of the coordinate system is implicit in this case.
You misunderstand - the structure of each particle has a lattice I guess, but each particle is randomly oriented relative to its neighbor, so there is no global orientation that we can observer by looking for light preferring one direction over another.
Are you sure? IMO, these coordinates will not be infinitely precise, lest they require infinite memory. Consequently, you would find that the space of possible angles and distances is in fact discrete, as it were defined by a lattice. The structure of the coordinate system is implicit in this case.