Borderless Goban

   

A borderless goban is a "double-round" rectangular grid unusual goban, which means, on whichever side you leave the board, you re-enter it at the opposite point. This geometry is also called toroidal. (That means, it's related to the surface of a torus, which is a donut with hole in it).

To speak more exactly, a borderless goban can be created by defining the two end points of each row (also, respectively, each column) to be adjacent. Therefore all points have four liberties each.

Any game position appears as if in an infinite two-dimensional square crystal structure with period of 19 points, and the actual board being just an arbitrary 19x19 section of the grid. You could shift this 19x19 board focus by any step, but, although the game probably will look different, it will be the same.


Properties

  • It's hard to get settled in the beginning, because with such a board no corners exist; every point is an "in-the-middle-of-the-board" point.
  • Of course, the board size doesn't have to be 19x19. Here you can see a borderless 9x9, for instance:
[Diagram]

Borderless 9x9

[Diagram]

Focus shifted (3 steps to the right)

[Diagram]

Another view (shifted again, up by 2 points)


Just a little exercise:

[Diagram]

All groups alive? help


The answer is Yes: if White doesn't connect. (Am I right? Some more conscious players, please check it again. I am a tired 9k (KGS) only. -- rubilia)


[Diagram]

19x19 example opening, 50 moves so far


[Diagram]

the same game, shifted view (A1 shifted to G5):


[2] If you're not used to borderless Go yet, you may like the doubled focus view:

[Diagram]

Redundant (18x18) view of the above 9x9


-- rubilia


This is a copy of the living page "Borderless Goban" at Sensei's Library.
(OC) 2005 the Authors, published under the OpenContent License V1.0.
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