On the physics, mathematics, and algorithms of knitting – What's floofy?

Siobhan Roberts, ‘Knitting Is Coding’ and Yarn Is Programmable in This Physics Lab, NYTimes, May 17, 2019.

Dr. Elisabetta Matsumoto, a physicist at Georgia Tech, "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.'"

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.” [...]

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.