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. _______________________________________________ computer-go mailing list computer-go@computer-go.org http://www.computer-go.org/mailman/listinfo/computer-go/
