‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab

For Elisabetta Matsumoto, knot theory is knit theory.

Elisabetta Matsumoto holds a Geared Cuboctahedral Jitterbug that she designed with mathematician Henry Segerman.Credit...Johnathon Kelso for The New York Times

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By Siobhan Roberts

BOSTON — On the eve of the American Physical Society's annual March meeting, a Sunday "stitch ‘n bitch" session convened during happy hour at a lobby bar of the Westin Boston Waterfront hotel.

Karen Daniels, a physicist at North Carolina State University, had tweeted notice of the meet-up earlier that day: "Are you a physicist into knitting, crocheting, or other fiber arts?" she asked. "I’ll be the one knitting a torus." (A torus is a mathematized doughnut; hers was inspired by a figure in a friend's scientific paper.)

At the bar, amid tables cluttered with balls of yarn, Dr. Daniels absorbed design advice from a group of specialized knitters, among them Elisabetta Matsumoto, an applied mathematician and physicist at the Georgia Institute of Technology and a co-host of the gathering.

For Dr. Matsumoto, knitting is more than a handicraft hobby with health benefits. She is embarking on a five-year project, "What a Tangled Web We Weave," funded by the National Science Foundation, to investigate the mathematics and mechanics of "the ancient technology known as knitting."

Some of the oldest examples date to the 11th century in Egypt. But despite generations of practical and experiential knowledge, the physical and mathematical properties of knitted fabric rarely are studied in a way that produces predictive models about how such fabrics behave.

Dr. Matsumoto argues that "knitting is coding" and that yarn is a programmable material. The potential dividends of her research range from wearable electronics to tissue scaffolding.

During the happy-hour meetup, she knitted a swatch illustrating a plastic surgery technique called Z-plasty. The swatch was for a talk she would deliver at 8 a.m. on Wednesday morning called "Twisted Topological Tangles." Scores of physicists turned up, despite a competing parallel session on "The Extreme Mechanics of Balloons."

"I’ve been knitting since I was a kid," Dr. Matsumoto told her (mostly male) audience. "That was the thing I did to get along with my mom when I was a teenager. It's just been a dream to take all of this stuff that I learned and played with as a child and turn it into something scientifically rigorous."

As a first step, her team is enumerating all possible knittable stitches: "There's going to be a countably infinite number. How to classify them is what we are working on now."

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The investigation is informed by the mathematical tradition of knot theory. A knot is a tangled circle — a circle embedded with crossings that cannot be untangled. (A circle with no crossings is an "unknot.")

"The knitted stitch is a whole series of slipknots, one after the other," said Dr. Matsumoto. Rows and columns of slipknots form a lattice pattern so regular that it is analogous to crystal structure and crystalline materials.

By way of knot theory, Dr. Matsumoto essentially is developing a knit theory: an alphabet of unit-cell stitches, a glossary of stitch combinations, and a grammar governing the knitted geometry and topology — the fabric's stretchiness, or its "emergent elasticity."

When discussing the emergent properties of knitting, Dr. Matsumoto sometimes makes reference to a butterfly, the vibrant blue morpho. Its color is optically emergent, the result not of chemical pigment but of structure. In effect, each wing is a metamaterial: covered in layers of nanosized scales, arranged in a pattern called a gyroid surface, the wing absorbs most wavelengths of light, but reflects blue.

Knitted fabric is also a metamaterial. A length of yarn is all but inelastic, but when configured in slipknots — in patterns of knits and purls — varying degrees of elasticity emerge.

"Just based on these two stitches, these two fundamental units, we can make a whole series of fabrics, and each of these fabrics has remarkably different elastic properties," Dr. Matsumoto told the audience.

She first combined her math-y and woolly mind-sets as a Ph.D. student, after admiring a friend's crocheted interpretation of the hyperbolic plane (curly kale is a vegetable example) and wondering how to do it differently.

"It irritated me that it wasn't isotropic," she recalled on the day before her talk. She could see where the crochet had begun, whereas a true hyperbolic plane should betray no starting point and no direction.

She thought, "I can fix that."

She crocheted a network of lace-like heptagons that produced a more uniform rendering. The hyperbolic plane has been her constant companion ever since. In April, she had a hyperbolic helicoid — a fantastically swirly helix, somewhat like a seashell — tattooed to her left shoulder.

During her talk, Dr. Matsumoto passed around her hand-knit swatches: stockinette (standard jersey, fairly stretchy, used for T-shirts); garter (stretchier); ribbing (stretchiest); and seed (not so stretchy, but one of her favorites).

A sizable fraction of her audience also flaunted their hand-knits — sweaters, hats, a water-bottle cozy, indeterminate works in progress. Dr. Matsumoto's most prized hand-knit creation is her "dragon of happiness" shawl (from a design by knitter Sharon Winsauer, a.k.a. the Crazy Lace Lady).

Knitting away for two months, Dr. Matsumoto encountered one stitch in the dragon's beard that she had never seen before.

"In the pattern for the dragon, there are all these crazy stitches," she said — stitches that took up not just a single cell on the pattern grid, but stretched across numerous cells, seeming to follow a horizontal array rather than the usual, vertical orientation.

Her team's knit theory will incorporate these and other stitch morphologies, as well as intentional stitch defects and constraints, such as how a yarn bends, twists and compresses; how many plies it has, how thick it is, and how "floofy."

Floofiness refers to a yarn's "halo area, where ephemeral fuzzy fibers stick out," Dr. Matsumoto said, and it changes the way two pieces of yarn interact with each other, their friction and energy exchange. "I’d love to write a paper using the word ‘floofy’ as a technical term."

Dr. Matsumoto's presentation opened a three-hour session entitled "Fabrics, Knits and Knots" — the first time that the subject had been addressed at the American Physical Society's annual meeting.

"Sabetta is spectacularly creative, and she is doing really mathematically sophisticated work," said Pedro Reis, the session organizer, who leads the Flexible Structures Laboratory at the Swiss Federal Institute of Technology in Lausanne. "She is also attracting a lot of people to the field who might not otherwise even think about science."

During his introductory remarks, Dr. Reis had a vexing encounter with an intertwined microphone cord. "This is a good example of why we really care about this topic," he said.

Dr. Reis grapples with the likes of long-overhand shoelace knotting, climbing knots, basket weaving, surgical sutures, and how to pass on the art of surgical-knot craftsmanship to robots. During the session, his lab mates described how they had used a CT scan to probe the internal structure of knot filaments and the friction that arises where filaments touch. After the meeting, Dr. Matsumoto sent him home with some of her swatches.

Derek Moulton, of the University of Oxford, mentioned variants of sailor's knots, DNA and protein knots, and worms that tie themselves into knots in order to minimize dehydration. He went on discuss "whether a knotted filament with zero points of self-contact may be realized physically." That is, can a knot exist wherein none of its crossings touch? (It can; try it at home with a strip of paper, or a cord.)

And Thomas Plumb-Reyes, an applied physicist at Harvard, presented his research on "Detangling Hair" to a standing-room-only audience.

"What is going on in tangled hair?" he asked. "What is the optimal combing strategy?"

Shashank Markande, a Ph.D. student working with Dr. Matsumoto, reported on their stitch classification work so far. Together, they had derived a conjecture: All knittable stitches must be ribbon knots. (A ribbon knot is a very technical tangle.) And they pondered the corollary: Are all ribbon knots knittable?

Back in February, Mr. Markande (who started knitting only recently for the sake of science) thought he’d found an example of an unknittable ribbon knot, using a knots-and-links software program called SnapPy. He sent Dr. Matsumoto a text message with a sketch: "Tell me if this can be knitted?"

Dr. Matsumoto was just heading out for a run, and by the time she returned, having manipulated the yarn every which way in her head, she had worked out an answer. "I think that can be knitted," she texted back. When Mr. Markande pressed her on how, she added: "It's knittable by our rules, but it isn't trivial to do with needles."

Mr. Markande said later, "I was pretty surprised. With my limited knowledge, I thought it could not be knitted. But Sabetta managed to knit it."

For the Tangled Web project, most of the experimental knitting is produced by a replica of a vintage 1970s knitting machine, the Taitexma Industrial and Home-Based Knitting Machine Model TH-860, which is operated by Krishma Singal, a doctoral student. The machine can also be programmed by punched cards — as was the Jacquard loom, invented in 1804 by Joseph Marie Jacquard and sometimes called the first digital technology.

Dr. Matsumoto's team likes to contemplate how stitch patterns provide code — more complex code than the 1s and 0s of binary — that creates the program for the elasticity and geometry of knitted fabric. The buzzword is "topological programmable materials," said postdoc Michael Dimitriyev.

He is working on a computer simulation of knitted fabric, inputting yarn properties and stitch topology, and outputting the geometry and elasticity of the real-life finished object. "I’m the killjoy that brings in elasticity," he likes to say.

The team's first paper, currently underway, will verify Dr. Dimitriyev's simulations against Ms. Singal's hard-copy swatches. Once the computer simulation is refined, Dr. Matsumoto and her collaborators can pull out equations and algorithms for knitted fabric behavior, which in turn could be put into physics engines for computer game graphics, or movies.

Pixar's "Brave" and "Monsters, Inc." showcased cutting-edge animation of hair and fur, but yarn has yet to have its time in the spotlight. Fabric animation is still very trial-and-error, and it requires time-intensive supercomputers to render.

"This could go in that direction," said Dr. Matsumoto. It's a good yarn, albeit just at the beginning, and still a bit floofy around the edges.

An earlier version of this article misstated the age of some of oldest examples of knitting. They date to the 11th century, not to the 11th century B.C.E.

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