[Frost1x]

I ran across this recently when a 2D based simulator described its world wrapping topology as being a torus. Turns out I took their metaphor a bit too far, assuming they actually considered geometry implications for world wrapping.

Spent awhile digging around until I found a euclidean 2-torus: the Clifford torus which can provide foundations to make the world wrapping metaphor a bit more accurate for flat 2D systems. It's still unknown to me if the authors actually had this in mind when they wrote the description of the wrapping system but it was certainly a fun side trek.

[fanf2]

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!

[dunkelheit]

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.