NickGotts wrote:Sure, an untwisted torus with any ratio between dimensions without a common factor will give the result you describe.

Yes, the path will cover the domain, but if the ratio of sides is near a ratio of small numbers, a glider's path will drift across the domain in small steps, and a large target will be hit near its edge. The golden ratio, as approximated by consecutive fibonacci numbers, is as "far" as possible from ratios of small numbers, and gives the best chance for a glider to hit a target of any size anywhere across its cross section.

For example, *WSSs would also not just go straight round to their starting point in the direction the twist was applied.

Good point, although *WSS become rarer relative to gliders as the domain is made more sparse.

(I think you could apply a twist in both directions.)

For a domain to be twisted in both directions, it would need to either include an extra small rectangle or have a rectangular cutout in one corner to fit together seamlessly. The latter would be a good option to add to Golly for this purpose. In Golly's help file it could be described like this:

:T30+5,20-2 -- torus with shifts of +5 on the horizontal edges and -2 on the vertical edges and with a 5x2 rectangle removed from one corner.

Edit: We want to specify the twist in both directions in such a way that both gliders and *WSS are equally likely to hit a target anywhere across its cross section. I think we can achieve this by using three or four consecutive fibonacci numbers as in these examples: T:89-55,55-34 (larger cutout) or T:89-34,55-21 (smaller cutout).