Colin Adams

Statement

At Bridges 2023, Barry Cipra and Paul Zorn introduced tri-colored carpets, which are carpets formed in the lower right quadrant of the plane woven out of vertical and horizontal strings in an alternating manner, with pixels colored using the rule that either all three colors at a crossing are distinct or the same. Students and I have extended this to p-colored carpets, and have been amazed at the beautiful patterns that appear. The simplest case is when p is an odd prime and the first entry in the top and left fringe is blue and the rest of the fringes are white. The more complicated patterns occur when you repeat the p colors periodically in the top and left fringe or when p is not a prime. The patterns are printed on 2'x2' rugs.

Artworks

This is a carpet with pixels determined by a 5-coloration rule from knot theory such that at each crossing in the woven carpet, the sum of the understrand labels equals the overstrand label modulo 5. This is a difference carpet, meaning the only non-white strands in the top fringe and the left fringe are blue strands in the first entry of each. We show only the first 625 x 625 pixels of what is in fact an infinite carpet covering the lower right quadrant of the plane.