Infinite Chess

If chess permits a virtually infinite variety of games, the rules of nature surely do. Science may be immortal after all. 

One of my favorite chess variants is called infinite chess, introduced to me by Tim Converse from the University of Chicago. In infinite chess, the game is played on an extremely large board or on one that extends arbitrarily in all directions. Queens, rooks, and bishops are permitted unlimited movement along their usual directions. 

Tim Converse notes that this game would be very different from standard chess. For one, pawns would become extremely unimportant, and probably many of the initial moves would be long moves by the major pieces. When playing on a very large chessboard, pawns will not be converted to queens because it would be difficult for pawns to reach the last row. In the infinite version, pawns never reach a last row of the board. 

If the chessboard were infinite—that is, played with no borders at all—the game could get very sparse as the pieces quickly disperse through the board. Infinite chess provides an interesting problem for game-playing computer programs, as the programs not only would have to limit the number of moves they look ahead (as usual), but would have to limit their spatial horizon as well. 

Although infinite chess is fascinating to contemplate, my favorite alternate chess game is called Too Many Bishops, a game I invented in 1992. In this weird variant, each player acquires an additional bishop before each turn. The bishop is placed on a position determined by the opponent. The game ends when a king is captured, or when a player cannot move due to the mob of bishops on the board, or when a player cannot add a bishop at the start of a turn because all squares are occu-... 

The dimeric structure of j8-CyD is most frequently observed as a building block of crystal structures. There are two types of arrangement of the dimer unit. In the head-to-head channel-type structure, the dimer unit is arranged to form an infinite linear channel. The other type is the layer-type structure, in which dimer units are arranged to form a chess-board-like pattern. Both ends of the dimer cavity are open to the intermolecular space in the adjacent layer. 

Fig. 29-3 Sections of infinite arrays of fibers illuminated alternatively with power + and —. The arrays are (a) one-dimensional, (b) columnar, (c) hexagonal and (d) chess board.

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