Lace in space

This series of work takes up bobbin lace, which is a textile technique originating in 16th-century Europe, made of intricately twisted, braided, and woven threads. In traditional lace, the strands were typically white cotton or linen. Bobbin lace was extremely valuable, with its value derived from the labor required to produce it rather than the raw materials. As such, lace was usually reserved for royalty, used on small and more intimate parts of garments such as cuffs and collars, or decorative items like trims on small doilies, or for covering babies. Early attempts to mechanize the production of bobbin lace were seen to devalue its specialness, to the extent that one unfortunate inventor was sentenced to death (Earnshaw, 1995). Across history, most machine-produced lace is actually a knit, which has a fundamentally different topology. Knits use self-intersecting loops to maintain their shape and facilitate fabrication. True bobbin lace does not self-intersect, requiring thousands of unique strands to span a modest area. In the 1800s, the emergence of Jacquard-style punch-card technology was integrated into the Leavers machine, which was the first and only machine to produce textiles topologically identical to hand-made lace. Today, very few Leavers machines remain in operation, as the specialized knowledge required to operate them is scarce, and the scalability of warp knits is more attractive to meet market demands.

While I find the history of bobbin lace and its complicated relationship with its making both rich and fascinating, this project began before I knew what bobbin lace was. My relationship with lace actually began when I stumbled upon two illustrations in Gottfried Semper’s Style in the Technical and Tectonic Arts, or Practical Aesthetics. In this text, Semper posits materials, fabrication, and the development of stylistic forms as intertwined entities. He argues that style in art and architecture emerges from the practical, material, and technical conditions of their making, rather than from abstract aesthetic ideals. Written in 1860 and translated into English in 2004, I have noticed, at least anecdotally, a growing interest in such material/structure/ornament holism in contemporary design thinking, particularly among architecture academics in the context of what I might call a crisis of fallout with Modernist aesthetics. I will not attempt to unpack the contemporaneity of Semper here, but the two drawings that caught my naive eye (and others’ less-naive eyes) were intended to depict generic textile swatches that have a specific topology, i.e. an arrangement of connected parts that arise from its structure, which consequently define certain spatial relationships, i.e. a design, and also appear decorative. Interested in these drawings, but knowing little about them beyond these observations, I scanned, enlarged, and printed them out, and then attempted to recreate the swatches with actual materials. Using the 2D printout as a template, I pinned some ribbon-like material I had in the studio at the time and glued the intersections to keep the network together. Upon unpinning, I was surprised to find how the resulting structures buckled out-of-plane. One took a wavy shape, while the other curled into a cylinder. Curious about the relationship between this form, the design, and material in these structures, I reached out to Prof. Sigrid Adriaenssens of the Form Finding Lab at Princeton University, and so began my research career in soft matter mechanics.

I soon learned that both textiles drawn by Semper are swatches of bobbin lace: two patterns commonly known as rose ground and tulle ground, which have repeating parts that make them useful for filling the background of a design and acting as a supporting net for figures. I find it interesting that bobbin lace, unlike other lace techniques, is worked continuously from top to bottom. As such, strands used in the background ultimately become the foreground. Shading is achieved by denser “stitch” patterning, such as “sewing,” where strands come together in a tight over-under grid that resembles plain-woven fabric and reads as solid. The backgrounds, or grounds, use periodicity and wider spacing between threads to recede.

Recognizing the prevalent symmetries in Semper’s ground patterns, I identified a basic unit that appeared to give both out-of-plane lace structures their shape. This unit we called the bigon, comprised of two elastic ribbons clamped at a fixed intersection angle. Bigons can be single or interlaced. Single bigons require clamping at nodes to stay open. Interlaced bigons can rotate freely at intersections because the interlaced configuration prevents the single bigons from closing. In a networked configuration, both bigons and interlaced bigons rely on the conservation of edge lengths between nodes to generate out-of-plane deformations. Notably, bobbin lace patterns also incorporate other n-gons. For instance, an interlaced bigon pair can be reinterpreted as a 4-gon bordered by 3-gons, with large interior angles preventing the structure from remaining planar. However, our study focused on the bigon and interlaced bigon motifs due to their distinctive mechanical behavior, which induces coupling among all surrounding n-gons, forming a single bistable unit. By toggling these bistable units between their up and down configurations, we constructed metastable networks capable of transitioning between multiple conformations, driven by the orientations of these interdependent elements.

Our JMPS paper explored these effects in 1D periodic chains of single bigons. We found that changing the angle at which the bigons are clamped (γ) changes the shape (α). Complexity arrises in the mechanical coupling between these elastic elements, making the number of states not strictly combinatorial, but dependent on the particular energy landscape.

(A lot) more information

The nature of this work shifted from physics/engineering to design and robotic assembly when I joined Stefana Parascho’s (now at EPFL) design research group during 2020-2021. To go deeper into the details of what emerged during that time, please see the following pages:

Future work would entail a systematic study of the mechanics of large, 2D lace networks, in particular, how manipulation of lattice geometry affects the energy landscape. For now, I have constructed desktop and meter-scale models posing as art projects. For more on the meter-scale sculpture, see “designing lace networks” (link here and above). On the following page, I am beginning to collate various models constructed at the desktop scale. One day, I hope this list will include out-of-plane lace garments:

Project outcomes

Exhibitions and events

Interdisciplinary workshop hosted at Princeton University with lace artist and mathematician Veronika Irvine. April 9-10, 2019.

“Interlaced Bigons” Joint Mathematics Meetings Art Exhibition, 2021.

“Lace in Space” Exhibition for the large lace sculpture and an online exhibition of lace artifacts from the Princeton University Art Museum, Princeton University. November 2, 2021.

“Bigon Network” Balancing Act, AIA NC Center for Architecture and Design, Raleigh, NC, 2023.

“Configurations of a six-bigon ring” Art of Science, Princeton University. May 2, 2023–present.

“Laced Periodic Surface” Connecting Artifacts 03, Komaba Museum, University of Tokyo, Tokyo, Japan. September 30 – November 26, 2023.

Publications

T. Yu, L. Dreier, F. Marmo, S. Gabriele, S. Parascho, S. Adriaenssens, “Numerical modeling of 2021 static equilibria and bifurcations in bigons and bigon rings”, Journal of Mechanics and Physics of Solids, DOI: 10.1016/j.jmps.2021.104459.

Press

EPrinceton: “Technique inspired lace making could someday weave structures space” 2021.

Grants

Support provided by Princeton University via the following programs:

• Princeton School of Engineering and Applied Science Project X Fund
• The Council for International Teaching and Research
• Magic Project, Princeton University Humanities Council
• University Committee on Research in the Humanities and Social Science