lew@ihuxr.UUCP (Lew Mammel, Jr.) (03/07/84)
In an earlier posting, I described how the game of Go could be regarded as being played on an infinite lattice with a unit cell made of four boards like this (a,b,c, and d are the corners of the board): d cc d b aa b b aa b d cc d I erroneously stated that this lattice had glide planes. The glide operation is to slide half a unit cell (one board) along the plane, and reflect across the plane. To make glide planes, we would have to use this unit cell: a bc d c da b b ad c d cb a The glide planes are along the center axes of the boards, not the edges. You could still play Go on this lattice, but it would not be equivalent to the standard game. Another arrangement is a simple square lattice of single boards. This creates the wrap around edge condition. We get the most general version of the edge condition by imagining two duplicate boards with the edge connections dangling. If we connect the dangling ends in pairs, we will have defined an edge condition. There are (4 * 19)! possibilities. These can be realized algorithmically on a single board by examining the mate of each edge point (two mates for the corners) when applying the rule of capture. This is reminiscent of the way metrics are specified in the early chapters of GRAVITATION. (See, physics!) I think there are 12 versions which can be realized with square lattices, remembering that all the boards must be duplicates (under rotations and reflections), and have the same edge neighbors. I think these form more interesting topologies than the randomly connected versions. ... standing on the rubber yellow line talking to myself, Lew Mammel, Jr. ihnp4!ihuxr!lew