Just recently (in fact it is still going on) there has been discussion on Arachne Lace list serve about mathematics and lace. It is focused on the work of Veronika Irvine, a lacemaker (bobbin lace) who holds a Master's Degree in Mathematics is is/was working on a PHD in computer science.
Click here for more information about Veronika Irvine: http://web.uvic.ca/~vmi/
The title to the paper is: "Developing a Mathematical Model for Bobbin Lace"
Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. An overview of how bobbin lace is made is presented and illustrated with a simple, traditional bookmark design. Research on the topology of textiles and braid theory form a base for the current work and is briey summarized. We define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search. Results of this new approach are presented and, by comparison to existing bobbin lace patterns, it is demonstrated that this model reveals new patterns that have never been seen before. Finally, we apply our new patterns to an original bookmark design and propose future areas for exploration
I pointed out to the discussion that there are some math ties to tatting too. A few years back, Patty Dowden introduced the tatting world to 'Hyperbolic Tatting' and taught it at the Minnesota IOLI Convention (so sorry I couldn't go to be in that class!).
Follow the following link to explore Patty Dowden's work on Hyperbolic Tatting:
Just recently I was in the Denver Art Museum Textile Gallery and they had some wonderful displays that introduced fiber/textiles as 'Art'. In the tatting display was a couple of small tatted bits of hyperbolic tatting. I faintly recall that Patty gave a workshop there...but could be completely wrong about that. I have a picture of the display and hyperbolic tatting in the previous blog posting.
I have been researching and playing around with the concept of Tesselation in my tatting design work. My last book, "MORE Fun with Split Ring Tatting", introduces that theme and features unique tatted designs with Tesselation in mind. However, "Tesselation" refers to designs 'made of identical shapes but the shapes must fit together without any gaps'. I have a few of these designs in my book. BUT....Lace is about the negative space (holes) enhancing the positive parts (the thread) in the design. Thus I came up with a new term: LACE TESSELATION. Many of my designs fit into that category.
You can see some of the designs on the front covers of the book at this address: www.TheShuttleSmith.com/books-for-sale/ There are more designs in the book.