I first encountered the idea of wrapping coordinates being equivalent to a torus when playing around with the Game of Life. I assumed that it was a topological equivalence as illustrated by https://commons.m.wikimedia.org/wiki/File:Torus_from_rectang... - I did not know there could be geometrically flat toruses!
Yes, it is common for 2D lattice simulations to use this topology. The rationale is that boundary effects get smeared across the whole lattice and thus are much smaller than if they were concentrated near, well, boundary.
