Toroidal Tessellations

Bead crochet bracelets have an allure that is hard to resist. For the wearer, adorned by the firm but pliable packing of beads into a sleek, snake-like skin, the appeal is both visual and tactile. For the crafter, the technique is meditatively repetitive and the bead color and texture choices endless. But for the mathematically minded, the greatest allure is in creating bracelet patterns. Behind the deceptively simple and uniform arrangement of beads is a subtle geometry that produces compelling design challenges and fascinating mathematical structures.

Inspired by the tessellated drawings and tiled pillars of M.C. Escher, each bracelet in this series has a pattern consisting of interlocking copies of a single shape in two to four colors. Designing such patterns for bead crochet bracelets is more challenging than designing them for prints or mosaics, both because the bracelet provides a narrower canvas and because the beads form a continuous spiral around the bracelet. This underlying spiral makes it especially challenging to align design motifs. With our original mathematical technique for bracelet design, we have tessellated our bracelets with natural and abstract forms, such as fish, lizards, stars and flowers.

To see more about the underlying mathematics and the art of bead crochet, look at Chapter 5 of Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist by Ellie Baker and Susan Goldstine.