CoM | Beading with Algorithms: Cellular Automata in Peyote Stitch

Beading with Algorithms: Cellular Automata in Peyote Stitch

Can you weave beads so that each new stitch you take depends upon what you have already beaded? To answer this question, we explore how the mathematical concept of one-dimensional cellular automata can be applied to beaded peyote stitch, in other words, beading with algorithms. Peyote stitch is a flat weave made with beads and thread that can be shaped into a variety of objects including jewelry and boxes. The peyote stitch grid is topologically equivalent to a grid of hexagons or a staggered row of squares, so applying the rules of cellular automata to this grid is similar yet different from elementary cellular automata. Algorithms provide a new way for bead weavers to select colors while weaving beads. With a traditional beading chart, you see the complete arrangement of colors before you ever start stitching. In contrast, by beading with algorithms, the mosaic of colors emerges automatically, bead by bead, or cell by cell, as you weave, hence the name, cellular automata. Many mathematical notions emerge including symmetry, reversibility, periodicity, modulus, automorphism, isomorphism, and counting.