Veronika Irvine
Bobbin lace is a 500 year old fibre art form in which delicate patterns are created by weaving together many threads to form an alternating braid. When I first learned to make bobbin lace I was struck by its mathematical nature. Like cellular automata, a small set of rules governs how threads can be combined but the results can be very complex. For my Ph.D. research, I have developed a mathematical model for bobbin lace using the pair (D,ζ) where D is a 2-regular directed graph embedded on a torus and ζ is a mapping from the vertices of D to a braid word. This has been a rewarding process providing me with perspective and motivation to explore new areas of math as well as a deeper understanding and insight into lace design and construction.
A fundamental component of bobbin lace is a small pattern, called a ground or filling, used to fill any closed shape by tessellation. To date, these patterns have been discovered through trial and error and extensive hands-on experience - a time consuming process. Applying an intelligent search algorithm to identify the D in (D,ζ), I have generated over 10^6 workable lace fillings. Aside from the daunting task of viewing all these patterns, the vast majority have minimal aesthetic appeal. Applying symmetry constraints to the search algorithm, I have filtered the results to find more interesting examples like the *442 orbifold shown here.
bottom left: Pattern derived from D. top right: Finished lace. diagonal: Thread detail showing ζ.