Single Comment

The alternating of colours is indeed to do with the two Bishop bindings, as each step of the Bishop moves comprises simultaneous steps in two out of forward/backward, left/right, and up/down. In other words the move is rotationally symmetric, so that a series of levels is the equivalent to a series of vertical planes. Now on the 2d board the colouring of the ranks alternates, and the colouring of the files alternates. A 2d plane with a rank or file entirely of white cells followed by one entirely of black cells, and so on, would look very odd, either as a whole board or a single plane of a 3d board. In that context a column of cells all the same colour would also be very odd.