This artwork is an outgrowth of an extended research project with Susan Goldstine on applications of mathematics to bead crochet. Our book, “Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist," outlines a new methodology for designing bead crochet patterns and describes a series of mathematically inspired design puzzles. Recently I've begun exploring design in fabric, a new medium with new constraints and new puzzles. Here, fabric printed with the infinitely repeating planar representation of a bead crochet pattern is sewn into an infinity scarf (topologically a torus). The construction, with hidden seams, involved stitching together opposite edges of a parallelogram and an interesting topology lesson on torus inversions.
This infinity scarf and bead crochet necklace are twin tori. The fabric design is (an elongated version of) the infinitely repeating planar pattern that a tiny explorer could map by charting the surface of the necklace in all directions (the universal cover of the beaded rope). The two colors, identical tessellated wave motifs, gradually transform from "calm" to "busy." The pattern at each step has an increasing "busyness" quotient (a measure of how much the individual beads in a fundamental tile differ in color from neighboring beads). The scarf, sewn from a parallelogram to create a mobius-like twisted torus, has a small hole in one seam so that it can be turned inside out to explore the puzzling behavior of torus inversions.