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Chess Mapping

What does a chess game look like when plotted to the xy plane? What would the set of all chess games look like?

Here’s what the Fisher Spassky 1972 Match #6 game looks like:

Here’s Morphy vs. Anderssen, 1858 9^th Match Game, Paris

The program uses a simple mapping algorithm. First a number from 1 to 64 is assigned to each space on the chess board, beginning at square a1 and ending at square h8.

On Move M, White moves from space S1 to space S2. Black moves from space S3 to S4. The plotted point at the end of this move is calculated as follows:

x = (S1*S1 + S2*S2 + S1*S2)*M*A1/2000
y = (S3*S3 + S4*S4 + S3*S4)*M*A2/2000

 (A1,A2) are rotating values through the sequence (1,1) (-1,1), (1,-1), (-1,-1). This allows the points to move in a confined area. Using the move multiple M assures that transposing moves will not lead to the same point.

 It would be interesting to plot thousands (even millions) of games to see what the resulting shape looks like. Do White wins look different from Black wins? Do well-played or poorly-played games have any special characteristics?

 The other map that could, of course, be created would use just the unique end points for each game. In the case of the Fischer Spassky game that end point is (94.0955, -20.6379). The area represented by the accumulation of these points might have interesting fractal properties and could arguably be considered a strange attractor for chess games.

 While the current formula makes it unlikely that two games would end on the same point The problem of overlapping games or endpoints could be solved by making the formulas a little more complex, by for example, appending unique infinite sequences to the value of each square.

 Still other interesting work might be done to explore other formulas, other coding schemes and more elegant graphic representations.
 

Mark Friedman September 28, 2004
xfpsi@aol.co
64 Herrada Road
Santa Fe, NM 87508