[computer-go] Big board. Torus ?

[alain Baeckeroot]

Le vendredi 23 février 2007 01:19, Matt Gokey a écrit :
> Here is a thought experiment to test: define the board only logically 
> using a graph (nodes and neighbor nodes).  No topological shape and no 
> mesh layout over any shape is needed.  If all nodes have exactly four 
> neighbors, there is no method or algorithm that you can run to find an 
> edge.  All nodes will look equivalent.
> 

I was partly wrong, but i maintain this board is anisotropic :
It contains squares and triangles, not equally spaced, all triangles
are on the borders.

Here is a simple algorithm to define the borders:
Starting from one node and moving to the next, you can go to the
Left, Front, Right or Back.
- Insides nodes : if you go always to the Right, in 4 steps you are back
   to the initial position.
- Near border nodes: there is one starting direction where you need only
   3 steps to go back if you always turn to the Right
- Border nodes: 9 steps.

QED number of neighbors is not enought to define the topology, (i suspect
this is well known ;-)

So i maintain it is a cylinder, with 2 borders which correspond to our
visual feeling.
Alain.