=Steve Witham this makes a way to wrap the sides of the board around for a game
(BTW we could curl up hexagonal boards too, and similarly for any even-gon.) Anyway, it seems a finite square board with edges identified would be logically equivalent to an infinite quilt of square patches in a regular board, each of which are initialized with a suitably rotated/reflected copy of the initial configuration. Does this mean that a doubly-twisted "purse" board will behave the same as an untwisted "torus" board?
kinks or anomalies that would snarl the game rules
Indeed this avoids local snarling, but curling up a CA generally mostly seems to introduce additional "global" phenomena that depend sensitively only on arbitrary details, such as the exact diameter of the universe along each axis.
=Keith F. Lynch It would be interesting if one of those was the topology of our universe.
I remember an ancient variant "Space War" that did this. It made shooting photon torpedoes "around the world" interesting -- especially if they interacted with the sun's gravity... A few years ago I saw a pop-sci article somewhere claiming that some cosmologists were trying to investigate this possibility by looking at the largest-scale density fluctuations. I think it may have even suggested something like a dodecahedron with opposite faces identified as being a model that was consistent with observations. Anybody else recall this?