Given how impossible I have found using the Rabbit piece as defined here I was disappointed as it is a good name for a piece it was rather wasted here. Its literary credentials are good - not just Lewis Carroll but Joel Chandler Harris and - in greater numbers - Richard Adams, A.A. Milne, and Beatrix Potter. Thus I began thinking that its name might be better deployed - with your consent, Tim - for another piece mixing orthogonal and diagonal steps, with a corresponding Hare piece swapping them round. If the compound of the two is not an existing piece, it could be called a Hatter in reference to Lewis Carroll.
After rejecting divergent pieces¹, pieces moving forward/backward as one Bent piece and sideways as another², and pieces making two turns a step apart in the middle³, I thought of retaining the double-bent theme but with both turns at the start. Thus the Rabbit might be defined as making a Mao move followed optionally by a second 45° turn and a Rook move, and the Hare as making a Moa move followed optionally by a second 45° turn and a Bishop move. In each case the second turn could be in either direction. These pieces are both interesting and manageable, and could quickly appear in a variant. There could even be a Contrarabbit and Contrahare with both bends at the end. Of course other CVP members might have even better ideas - including yourself - so if you are willing to open up the question of what kind of piece to call Rabbit it would interestiung to read such cuggestions.
¹ These tend to have servile names, and neither real nor literary lagomorphs are noted for servility. Better suiting divergent pieces involving a Bent or Double-Bent move would be names of the great many dog breeds(although Foxhound and Wolfhound are already taken for Bishop compounds).
² This felt too contrived to me.
³ Still too strong, despite being blockable and barred from moving less than three steps.
After rejecting divergent pieces¹, pieces moving forward/backward as one Bent piece and sideways as another², and pieces making two turns a step apart in the middle³, I thought of retaining the double-bent theme but with both turns at the start. Thus the Rabbit might be defined as making a Mao move followed optionally by a second 45° turn and a Rook move, and the Hare as making a Moa move followed optionally by a second 45° turn and a Bishop move. In each case the second turn could be in either direction. These pieces are both interesting and manageable, and could quickly appear in a variant. There could even be a Contrarabbit and Contrahare with both bends at the end. Of course other CVP members might have even better ideas - including yourself - so if you are willing to open up the question of what kind of piece to call Rabbit it would interestiung to read such cuggestions.
¹ These tend to have servile names, and neither real nor literary lagomorphs are noted for servility. Better suiting divergent pieces involving a Bent or Double-Bent move would be names of the great many dog breeds(although Foxhound and Wolfhound are already taken for Bishop compounds).
² This felt too contrived to me.
³ Still too strong, despite being blockable and barred from moving less than three steps.