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Chess on an Infinite Plane. Chess game with no boundaries (infinite board), and Guard, Chancellor, and Hawk. () [All Comments] [Add Comment or Rating]
Aurelian Florea wrote on Sun, Aug 6, 2023 10:18 AM UTC in reply to Aurelian Florea from Tue Jan 9 2018 09:30 AM:

While contemplating the discussion  here: https://www.chessvariants.com/index/listcomments.php?id=48814 about (5,x) pieces, with x=1..4, I remembered V. Reinhart's Huygens piece, and  I came up with one of my own piece on an infinite plane. A compound of all leapers (m,n) with m>n where m is any prime number strictly larger  than 1 and n are all the numbers from 1 to m-1. An then let all the leaps ride. The branches will not intersect with each other. While thinking this I came up with a compund leaper where the (m,n) pair is any ireducible fraction. I could not realize yet if this yields a rider where the branches don't interesect each other. Any other thoughts on this topic?