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George Duke wrote on Thu, Jun 18, 2009 11:55 PM UTC:
Totally disregarding Pawn and King (&Q), with just 6 identifiable piece-types, we can reach from the center square of enclosing 15x15 set of squares, numbering 225 squares every oblique one of them logically. Adrian King's large Jupiter is 16x16 so 225 squares covered by 6 pieces is pretty sweeping. Falcon 3, Scorpion 4, Dragon 5, Phoenix 6, Roc 7. Those numbers are steps, and Knight of course the other guy. Subtract one for # squares per general direction: 2,3,4,5,6. So it's a complete re-organization with rather few pieces. Roc moves from a starting square to one quadrant any of (6+6) or 12 squares, half on each side of the Bishop radial, within the surrounding 15x15 set of squares, with Roc squares all on that perimeter and excluding only Rook and Bishop destinations. I would say multi-path as a category is about equivalent to all of Man & Beasts 1 - 21 combined, if they were to be developed for the sake of proliferation Actually multi-path would far exceed all non-leapers, because any already-defined piece can be extended with new pathway(s)--multi-pathing. So it would be idle to tuck a few of them into Bent Riders etc., MAB13; but please do so tentatively until we add entire M&B chapters for plural pathways, drawing on my article ''Multi-path Chess Pieces.'' For example, if wanting to avoid leapers, we eliminate both Giraffe(1,4) and Antelope(3,4) for way of Scorpion: one piece multipath. We eliminate Zemel(1,5), Vine (2,5), Gemel(3,5), and Rector(4,5) to make way for one replacement who goes wherever all they go, Dragon: one piece multipath five-stepping. Likewise, instead of distinct piece separately for each of (1,6) (2,6) (3,6) (4,6) (5,6), only necessary is Phoenix six-stepping. And so on for Roc's replacing the potential six separate leapers to his squares seven steps each by several pathways. Multi-path does not particularly trump leapers though the former are easier to visualise in a group; they should all coexist. Alternatively, we might want compound leapers, such as on narrow boards, where fixed length inherent in the regular multi-path units above is an obstacle. There are three variables: # arrival squares, # pathways, # steps. Centred on 8x10 Falcon in all directions has 16 arrival squares exactly the same as Rook by design.