Go on other topologies? (not realistic feature request)

Hi, this is not really a feature request, just an idea I had that maybe other people would find interesting. So, Go is normally played on a plane. However there are other shapes onto which we can naturally place grids (I think this basically comes down to shapes which can be made as the quotient space of the plane and the free action of a group… there might be more requirements though). For example, one could place a grid on a cylinder, and then play go on that grid. Of course, it would be a little more challenging to make a cylindrical go board, but it would be possible I suppose with magnets and what not. However, on a computer, its pretty simple to visualize. Take one of the dimensions, say the horizontal one, and simply dont have edges there, so the board would look like a strip 19 high and scrolling off to infinity on either side. Then when a stone is placed on the board, it appears repeating every 19 steps to either side. Does that make sense?

Other shapes could be accomplished too. For example to do the torus, we would do something similar except in both dimensions. So, we would play on an “infinite” grid, but stones would be repeated every 19 places up, down, left and right. Heck, we could do non-orientable surfaces as well. For a moebius strip, we take the same method as the cylinder but reflect the position vertically every other repetition. Lastly for the Klein bottle we would just repeat that in both dimensions, so the stones position would reflect horizontally when being repeated vertically and vertically when being repeated horizontally. Does that makes sense? It would be a cool option methinks, but maybe only for a very odd subset of people… hmmm kinda want to build a go app to see how this would play. I am not even sure if the game would be any good without the edges, but there is only one way to find out…

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Little Golem implements toroidal go (11x11 board only), so you can get some idea of how that kind of thing progresses by looking on games there. For example, this one.

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or 3-d go with tetrahedrons so that each stone still has 4 liberties?

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In general, the game can be extended to arbitrary graphs, with each vertex being a valid point to play, and edges indicating adjacency. Of course, many variations upon this idea and corresponding ways to visualize these variants have been considered.

Most of these variants have not been deeply studied, however, it’s clear that the connectivity of the graph (i.e., the degree and whether “edges” exist) have a large impact on the nature of the game. The graph does not need to be planar (except to maybe ease visualization) or correspond to an orientable surface, nor would the presence/absence of these properties alone necessarily effect the game drastically. For example, go on the outside of a cylinder might not be too fundamentally different than go on a moebius strip.

The ease of visualizing of the playing surface is whole other question. You would not have to render an “infinite” surface with repeating stones, just clearly representing where a finite board connects/“wraps around” would be sufficient.

http://senseis.xmp.net/?UnusualGobans
(see links at bottom for software that supports particular variants)

http://senseis.xmp.net/?BorderlessGoban
(includes a link to a torodial go program)

This Wikipedia page even has a picture of someone playing “diamond go” on a 3D tetrahedral lattice as @Samraku suggested.

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