Sunday, November 22, 2020

[fjrzunlu] piece power function

how many more squares can a given (fairy) chess piece reach in N+1 moves over N moves?  first differences of range function.

for wazir, ferz, dabbaba, or alfil, on an otherwise empty infinite board, the sequence is 4, 8, 12,... (multiples of 4).

king: 8 16 24 ... (multiples of 8).

to do: knight.

to do: compute for a finite board.  average over possible initial positions.

these sequences allow comparing different fairy chess pieces.  also more dimensions, other grids and graphs.

probably only useful for non-ranged pieces.

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