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Prince. 8x8x8 3-D variant with new pieces. (8x8x8, Cells: 512) [All Comments] [Add Comment or Rating]
Joe Joyce wrote on 2009-06-27 UTC
As I don't think Gavin will mind, and since you insist, George, I'll transfer this part of the discussion from Charles Gilman's MAB Overview and glossary Comments section to here. 

Multipath is a too-inclusive term for a good definition of a piece. Let's consider some multipath pieces. First, the Falcon - it has 16 destination squares, all at range 3, and there are 3 paths to each target square. The Falcon is, however, an 'Or' piece; it takes this path OR that path OR this other path, traversing only a single physical route from origin to destination in its actual move. The 'hook rook', the 'planar' piece of Chris Witham, is similar to the falcon, in that it has 2 possible routes to any destination square, and uses only one to go from origin to destination. In terms of physics, these pieces are both representative of the 'billiard ball' theory of atomic particles. While they may change directions on the trip, the pieces travel a well-defined and measurable path from beginning to end. As long as 1 path is open, they are good to go.

The 'planar rook' of Prince is like a quantum particle. It travels, and must travel, every possible minimal path simultaneously in going from origin to destination, and thus it can be blocked by a single piece anywhere in the area over which it travels. This is an 'And' multipath piece. It travels by this path And that path And the other path And ... and that's why it's so blockable. This refines the 'Multipath' classification.

One of the key features of planar pieces in Prince is the shape of the shadow that blocks a planar piece, a rook, say. In Prince, it is always a rectangular shadow that starts at the near edge of the blocking square and runs perpendicular to the line between the 2 pieces that blocks the planar rook in Prince. This is not the only possible shape for a shadow. Another very reasonable shape would be a cone, with the tip being the blocking square and the triangular shadow spreading out directly 'behind' the block, away from the planar piece. This would allow a planar rook to penetrate past the first obstacle. Varying the angle of opening of the shadow would give other effects, including bending the shadow back toward the planar piece by making the angle of opening greater than 180 degrees. The current angle of opening for a block's shadow of the planar rook is exactly 180 degrees. And I would argue this is yet another way to classify planar pieces. 

Charles, if you are following this, would any of this comment be pertinent to any definitions or classifications you might use?