Emily Cannon

Undergraduate Student
Randolph-Macon College
Ashland, Virginia, USA

Fall 2018, I audited a course at Randolph-Macon College taught by Dr. Eve Torrence called Making Mathematics. In that course, based on Crafting Conundrums, by Ellie Baker and Susan Goldstine, I learned that various mathematical concepts could be represented by a fiber arts technique called bead crochet. I absolutely loved the course; even afterward, I stuck with it. When I studied abroad in Japan the following spring, I had the opportunity to purchase lots of my favorite seed beads, and I made my first necklace. Last fall, when it came time to start my mathematics capstone, I knew I wanted to do something with bead crochet. Thus, after doing a great deal of searching for ideas, I decided on trying to represent fractals with this technique.

Beaded Jewelry Set with Fractal Step Designs
Beaded Jewelry Set with Fractal Step Designs
29 x 18 x 1 cm
Size 11 Miyuki Delica glass seed beads, and polyester thread

The larger necklace, made with 8,160 beads, shows iterations of the Sierpinski triangle; the design of the third step is based on Pascal's triangle colored modulo 2, and the other steps stem from that design. Matching earrings were created using peyote stitch. The choker is a representation of the Cantor set, with six steps and roughly 2,916 beads. Each step twists around the choker, following the technique's natural spiral. The remaining pair of earrings shows the combination of the generators of two square fractals. This idea came from a paper by Cotton, McLeman, and Pinchock: "On Combining and Convolving Fractals," The College Mathematics Journal, March 2015. The two generators are on top, the two possible combinations below.