Check out this 2006 blog post by Paul Burgess, which explains the rules of a chess variant called singularity chess (hat tip: @pickover). Reverend Burgess, an ordained Presbyterian minister in rural Iowa, had originally discovered this variant when he was a graduate student at the University of Wisconsin-Madison in the late 1970s/early 1980s. Below the fold are some photographic and literary excerpts from Burgess’s beautiful post:
“You’ll notice that the ‘squares’ on the board are not really square— they range from more or less square to semicircular. Even though the ‘squares’ differ in shape, each ‘square’ has four sides and four corners.
“Even the two semicircular ‘squares’ at the center of the board have four sides and four corners. (Corners indicated above in red.) These two ‘squares’ share two sides and three corners in common. The corner between them which lies at the very center of the board is the singularity from which this chess variation takes its name.
“Since the board layout is a ‘curved space,’ straight moves and diagonal moves have to be defined locally instead of globally. A straight move can be defined as a move which enters a ‘square’ through one side, and may continue on to exit the ‘square’ through the opposite (nonadjacent) side. A diagonal move can be defined as a move which enters a ‘square’ through one corner, and may continue on to exit the ‘square’ through the opposite (nonadjacent) corner.
“This leads to some long-distance moves which are anything but straight as we think of straight. Notice how the rook’s move can take it looping around the center of the board, and right back like a boomerang to the same side of the board it started from.
“The knight’s move likewise is distorted in an almost psychedelic fashion. (First knight’s moves in white, second knight’s moves in yellow.)
“I don’t recall exactly how the pawns moved. It seems to me that a rook’s pawn could end up ‘curving’ if it went two spaces on its first move— probably not wise for it to move that far while there are still enemy pieces in that vicinity.”
You may read Rev. Burgess’s entire “singularity chess” blog post here. Also, check out his short-lived (2004 to 2007) blog here.