Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 exptools 1/6/84; site ihuxr.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!ihuxr!lew From: lew@ihuxr.UUCP (Lew Mammel, Jr.) Newsgroups: net.games.go,net.physics Subject: Solid State Go Message-ID: <949@ihuxr.UUCP> Date: Mon, 5-Mar-84 18:33:00 EST Article-I.D.: ihuxr.949 Posted: Mon Mar 5 18:33:00 1984 Date-Received: Tue, 6-Mar-84 03:35:12 EST Organization: AT&T Bell Labs, Naperville, IL Lines: 33 Have you ever noticed that Go can be regarded as being played on an infinite square lattice with a 38x38 unit cell and two sets of glide planes with period 19 ? The unit cell contains four boards, a copy of the actual board, and two copies of its mirror image. they fit together like this: 4 . . . . . . . . 3 . . O . . O . . 2 . . O . . O . . 1 . . X X X X . . 1 . . X X X X . . 2 . . O . . O . . 3 . . O . . O . . 4 . . . . . . . . D C B A A B C D The actual board is on the upper right, and its copy is on the lower left, rotated by 180 degrees. If this unit cell is repeated, the other corners will show the same symmetry. The board itself forms a primitive cell, which generates the infinite lattice by repeated application of the two glide operations. This scheme replaces the edge condition with a repetition pattern for each move, preserving the rule of capture. Moves near the corner will form a lattice of rectangles with period 38. A move at the center forms a square lattice with period 19. This doesn't really lead anywhere, but I think it's interesting. Lew Mammel, Jr. ihnp4!ihuxr!lew