zenorogue,
@zenorogue@mathstodon.xyz avatar

A game of Go on a hyperbolic manifold, played in the HyperRogue discord server, ended like this.

zenorogue,
@zenorogue@mathstodon.xyz avatar

An animation of this game. (In the end, dead groups are removed for scoring purposes.)

Thanks to tres14159 on Twitter for the idea of the animation, and to @henryseg for the suggestion to make the stones larger. This is not a regular tiling, so some stones touch, but in some cases the distances between intersections are larger.

video/mp4

chanezon,

@zenorogue @henryseg very cool!

henryseg,
@henryseg@mathstodon.xyz avatar

@zenorogue Aesthetically, I’d want the stones to be a bit bigger, almost or even touching, to make it easier to see the groups. Also, even toroidal go is very different from standard go due to the lack of boundary. It would be interesting to see a game played on a hyperbolic board in the shape of a suitable right angled polygon.

irving,
@irving@mastodon.social avatar

@henryseg @zenorogue I played a game of torus go once, against a player a few stones weaker, and won the entire board (harder to establish a live group in the absence of sides and corners).

zenorogue,
@zenorogue@mathstodon.xyz avatar

@henryseg Agreed about sizes, thanks!

I have played Go on torus and it was quite satisfying, I feel that the boundary makes Go less pure, so to say (by having special strategies for edges and corners). (Similarly stairways in roguelikes are less pure, I am happy that they are avoided in HyperRogue :)

henryseg,
@henryseg@mathstodon.xyz avatar

@zenorogue I guess the most pure version of the game is played on a graph that is randomly chosen at the start of each game.

bo,
@bo@social.coop avatar

@henryseg @zenorogue while not as cool as a non Euclidean board, have you seen Custom Goban? Can play arbitrary map shapes and the introduction of many corner-like scenarios can make for quite a surprising and weird game

zenorogue,
@zenorogue@mathstodon.xyz avatar

@henryseg Also forgot to mention: bounded subsets of H^2 have this property that most area is close to the boundary, so the boundary effects would be more prominent than in the Euclidean case... any idea of a suitable right angled polygon and a tessellation of it?

henryseg,
@henryseg@mathstodon.xyz avatar

@zenorogue You could go as far as making a 15+4 puzzle style board with five 9x9 boards arranged around a single pentagon. Does every pentagon add an extra corner to the board?

irving,
@irving@mastodon.social avatar

@henryseg @zenorogue Or on the Rado graph! But that’s probably pretty boring, I suppose.

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