Equivalence relation/Accessibility/Chess board/Exercise

We consider the chess pieces rook, bishop, knight, and donkey, together with their allowed moves on a ${}8\times 8$-chess board. A donkey is allowed to move a double step forwards, backwards, to the right, and to the left. Every piece defines an equivalence relation on the ${}64$ square; two squares are equivalent if one square can be reached from the other square by finitely many moves of this piece. Determine for every of these chess pieces the corresponding equivalence relation, and the equivalence classes. How does it look on a ${}3\times 3$-chess board?

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