George Duke wrote on Fri, Nov 15, 2013 06:44 PM UTC:
Atomic Chess pieces include Wazir, Ferz, Dabbabah, and Alfil. There are
several atomic categorizations possible according to how far away from
starting square to include and whether to allow jumping directly to farther
arrival square. These Betzan Atoms are of great interest to CVers, but
Fundamental Chess pieces are of utmost importance to players.
OrthoChess has used three of the four Fundamental Chess pieces for 500
years: Knight, Rook, and Bishop. NRB comprehensively reach squares
different one from another out to 5x5 surrounding departure square as
centre. Besides, N, R, B each have their own unique modality. The fourth fundamental, Falcon, reaches unique squares out to 7x7. Falcon
cannot leap like Knight and just slides a fixed three-length, but neither
as Rook nor as Bishop, Falcon alone having multiple pathways, namely three.
Though not employed regularly, Falcon is actually mathematically the first
of the four Fundamentals. It is because implicit in Falcon's one and two
orthogonal part-steps are all of Wazir, Dabbabah, and Rook. Also implicit
in Falcon's one and two diagonal part-steps are all of Ferz, Alfil, and
Bishop. Also implicit in Falcon's damped non-leaping oblique
directionality is fellow-oblique Knight. So the order of derivation by
true protogeometric application is: Falcon->Knight->Rook->Bishop.
