H. G. Muller wrote on Tue, Oct 11, 2016 03:29 PM UTC:
You mean two hex-rook moves with an angle of 120degrees between the two? So something like this:
. . R C B C R . .
Z C R N N R C Z
Z B N R F R N B Z
C N F W W F N C
R R R W O W R R R
C N F W W F N C
Z B N R F R N B Z
. C R N N R C Z
. . R C B C R . .
The C definitely is not color bound then: from O it can reach two cells that are 2 hex-rook steps removed from each other. Do that twice, and you move four hex-rook steps. OTOH there also are C cells that are 5 hex-rook steps from each other. So you can move a single hex-rook step in 6 moves. And if you can do a single hex-rook steps you can go anywhere. Hex-zebras alread kan reach an adjacent cell in two moves.
The 12 moves that oblique leapers have can be split into two chiral sets of 6: the right-bending and left-bending. Pieces that only have the 6 moves from one such group always suffer a form of meta-color binding: they can make a triangle by making 3 leaps at angles of 60 degrees to define a triangle, and the plane can then be tiled with such triangles (sharing the corners). These corners are then the only cells that can be reached. Pieces with non-oblique moves, i.e. (N,0)- and (N,N)-leapers always have only 6 moves, and except for the hex-wazir (which makes the smallest possible step,and thus sever skips anything) they will all have high-order color binding.
You mean two hex-rook moves with an angle of 120degrees between the two? So something like this:
The C definitely is not color bound then: from O it can reach two cells that are 2 hex-rook steps removed from each other. Do that twice, and you move four hex-rook steps. OTOH there also are C cells that are 5 hex-rook steps from each other. So you can move a single hex-rook step in 6 moves. And if you can do a single hex-rook steps you can go anywhere. Hex-zebras alread kan reach an adjacent cell in two moves.
The 12 moves that oblique leapers have can be split into two chiral sets of 6: the right-bending and left-bending. Pieces that only have the 6 moves from one such group always suffer a form of meta-color binding: they can make a triangle by making 3 leaps at angles of 60 degrees to define a triangle, and the plane can then be tiled with such triangles (sharing the corners). These corners are then the only cells that can be reached. Pieces with non-oblique moves, i.e. (N,0)- and (N,N)-leapers always have only 6 moves, and except for the hex-wazir (which makes the smallest possible step,and thus sever skips anything) they will all have high-order color binding.