H. G. Muller wrote on Sat, Jun 17, 2023 05:49 AM UTC:
Many of the early postings are about normal Crabriders; only one mentions crooked ones. I don't think anyone would need an explanation or diagram to understand how a normal Crabrider moves.
This discussion on 'high-order color alternation' is interesting, btw. I wonder how far this can be pushed. In other words, which fixed move pattern would need the most moves to return to the same square? I suppose there is no limit: by combining moves with incommensurate strides in one dimension you force the return duration in that dimension to be their sum. E.g. fNbH (or fNbZ) are color alternating, but since their vertical stride is +2 or -3 it would need 5 moves to return to the same rank, and 10 moves to return to the same square. Returning to the same file could take longer if there was left-right asymmetry. With only a +2 and -1 stride it would take 3 moves. So a lfNrfAlbCrnZ would take 15 moves to return to the same square.
[Edit] One can also increase the cycle by creating the left-right asymmetry by removing one if the moves. E.g. a 'Fiddler Crab', lfbsN needs 12 moves to return to its starting square.
Many of the early postings are about normal Crabriders; only one mentions crooked ones. I don't think anyone would need an explanation or diagram to understand how a normal Crabrider moves.
This discussion on 'high-order color alternation' is interesting, btw. I wonder how far this can be pushed. In other words, which fixed move pattern would need the most moves to return to the same square? I suppose there is no limit: by combining moves with incommensurate strides in one dimension you force the return duration in that dimension to be their sum. E.g. fNbH (or fNbZ) are color alternating, but since their vertical stride is +2 or -3 it would need 5 moves to return to the same rank, and 10 moves to return to the same square. Returning to the same file could take longer if there was left-right asymmetry. With only a +2 and -1 stride it would take 3 moves. So a lfNrfAlbCrnZ would take 15 moves to return to the same square.
[Edit] One can also increase the cycle by creating the left-right asymmetry by removing one if the moves. E.g. a 'Fiddler Crab', lfbsN needs 12 moves to return to its starting square.