Veronika Irvine

Post Doctoral Fellow in Computer Science
University of Waterloo
Waterloo, Canada

Bobbin lace, a 500-year-old art form, features delicate patterns formed by alternating braids.

Veronika is a computer scientist and a lacemaker. She has developed a mathematical model to describe bobbin lace tessellations as a drawing of a 2-regular directed graph on a torus and a mapping from the vertices of the graph to braid words. Based on this model, she has used a combinatorial search to look for new patterns for this fiber art form. Having found millions of matches, she has refined the algorithmic search to look for patterns with specific types of symmetry. In particular, she has sought out symmetries that are relatively rare or unknown in traditional practice such as six and three fold mirrors and rotations.

Delle Caustiche (Sagittarius Star Cloud)
Delle Caustiche (Sagittarius Star Cloud)
40 x 40 x 40 cm
Cotton thread and copper wire

I used an algorithmic search to find a lace pattern graph with *632 symmetry. This required relaxing the usual monotonic path of threads in a braid while still maintaining the partial order of crossings. A mapping from the vertices of the graph drawing to braid words was chosen resulting in a 2-colour *632/632 symmetry. The pattern, originally on hexagonal grid, was mapped to a disk with the constraint that edge length differences were minimized for each triangle. Three full revolutions of the lace, in cotton thread supported by a copper wire frame, are connected start to end (forms a link from braids) without introducing twists and formed into an undulating shape in 3D inspired by "Three Waves Meeting" (Erik and Martin Demaine, 2009).