[vachnlwl] changing square colors every move

knight is the only orthodox chess piece which must change square color every move (parity).  in fairy chess, wazir is another.

for normal movement (not its two square initial move nor diagonal capture), pawn also changes square colors every move.

next simplest are the (0,3) leaper (three-leaper) which obviously cannot reach all squares, and the (2,3) leaper (zebra) which can reach any square.

compose chess puzzles that rely on this parity.  maybe in some chess variant in which all pieces must move every turn.  triangulation is a related technique in endgames.

if a chessboard were colored 4 different colors in a certain way, ferz would also change square color every turn, alternating between 2 of the 4 colors.