Knots such as these form the basic unit of knot theory. Image credit: Matematica (IME/USP)/Rodrigo Tetsuo Argenton

Markande can reduce four common types of stitch —knit, purl, and their twisted varieties— to different knots that have already been studied extensively by mathematicians. Of course, you would hardly consider the bow in your shoelaces to be a piece of fabric, so Markande is developing an algorithm to extrapolate upwards; what happens when you combine 10 such knots? 100? The typical sweater contains on the order of 100,000 stitches, making Markande’s work anything but trivial.



The key comes with the periodicity of knitted fabric. Although many knitters add complicated and irregular designs like cables for fashion or additional structure, fundamentally the cloth is produced by repeating the same unit structure many times. This could be a single stitch (for example, stockinette stitch is produced using only knit stitches) or a combination of stitches (alternating knit and purl stitches can produce a seed stitch or a rib stitch). Each of these units gives the final fabric a different property; rib stitch is extraordinarily elastic in a single direction, which is why it is commonly used for necklines and socks, while seed stitch results in a denser, stiffer final product.



Mosstickning knitting pattern (left) versus a ribbing knitting pattern (right) Of course, to truly characterize the fabric it is important to consider the properties on a macro scale as well as by the single stitches. Another graduate student, Krishma Singal, is working closely with Dimitriyev and Matsumoto to develop protocols to test the properties of each stitch like elasticity and strength. “We’re kind of a strange theory group mashed up with a makerspace,” Dimitriyev says of the lab, which is full of yarn and needles, 3D printed testing apparatus, even a vintage knitting machine. “We’re taking a holistic approach.”



That holistic approach may just be the key to bringing the theory out of the lab and into industry. To hear the researchers describe it, the possible applications are nearly boundless. For example, animators for video games and CGI tend to avoid simulating knitted fabric, preferring instead a simple woven material. “Nobody has found a really good, efficient way of simulating these fabrics,” Dimitriyev says. Instead they usually just add texture to their woven fabric simulations, which makes things like sweaters appear…. not quite right.



Although it would be possible to build up a much more realistic simulation from the stitch analysis that Markande is working on, Dimitriyev thinks there should be a simpler way. “That’s like doing an all-particle molecular dynamics simulation of some material like water” he says. “Why would you simulate all the particles in a glass of water that’s being poured when you have the Navier-Stokes equations?” Instead, he is working on the knitted counterpart to fluid dynamics, a set of partial differential equations that succinctly and accurately describes the textile’s behavior.



The lab has even more grandiose ideas for their research, however. As Dimitriyev points out, knitters can effectively “program” their fabrics by manipulating the properties of each stitch. “Not only are these materials programmable,” he says, “they have an established coding language.” In fact, the conventions are so well-established that the vintage knitting machine in the Matsumoto lab takes instructions from punch cards, acting much like an early computer.



Punch cards used in the Matsumoto lab's vintage knitting machine Dimitriyev says that Markande’s attention to the smallest unit of knitted fabric, the knot, is like putting together the alphabet that will eventually lead to much higher-level functionality. Thinking forward to that functionality, Markande hopes that his work will help with the development of



Although the field is rich, only a handful of labs worldwide currently focus on the science of knitting. On the other hand, textile engineers and knitting enthusiasts alike have spent centuries building up vast stores of knowledge. So the next time you don that sweater, maybe take a minute to give this feat of engineering the admiration it deserves.

—Eleanor Hook







Markande can reduce four common types of stitch —knit, purl, and their twisted varieties— to different knots that have already been studied extensively by mathematicians. Of course, you would hardly consider the bow in your shoelaces to be a piece of fabric, so Markande is developing an algorithm to extrapolate upwards; what happens when you combine 10 such knots? 100? The typical sweater contains on the order of 100,000 stitches, making Markande’s work anything but trivial.The key comes with the periodicity of knitted fabric. Although many knitters add complicated and irregular designs like cables for fashion or additional structure, fundamentally the cloth is produced by repeating the same unit structure many times. This could be a single stitch (for example, stockinette stitch is produced using only knit stitches) or a combination of stitches (alternating knit and purl stitches can produce a seed stitch or a rib stitch). Each of these units gives the final fabric a different property; rib stitch is extraordinarily elastic in a single direction, which is why it is commonly used for necklines and socks, while seed stitch results in a denser, stiffer final product.Of course, to truly characterize the fabric it is important to consider the properties on a macro scale as well as by the single stitches. Another graduate student, Krishma Singal, is working closely with Dimitriyev and Matsumoto to develop protocols to test the properties of each stitch like elasticity and strength. “We’re kind of a strange theory group mashed up with a makerspace,” Dimitriyev says of the lab, which is full of yarn and needles, 3D printed testing apparatus, even a vintage knitting machine. “We’re taking a holistic approach.”That holistic approach may just be the key to bringing the theory out of the lab and into industry. To hear the researchers describe it, the possible applications are nearly boundless. For example, animators for video games and CGI tend to avoid simulating knitted fabric, preferring instead a simple woven material. “Nobody has found a really good, efficient way of simulating these fabrics,” Dimitriyev says. Instead they usually just add texture to their woven fabric simulations, which makes things like sweaters appear…. not quite right.Although it would be possible to build up a much more realistic simulation from the stitch analysis that Markande is working on, Dimitriyev thinks there should be a simpler way. “That’s like doing an all-particle molecular dynamics simulation of some material like water” he says. “Why would you simulate all the particles in a glass of water that’s being poured when you have the Navier-Stokes equations?” Instead, he is working on the knitted counterpart to fluid dynamics, a set of partial differential equations that succinctly and accurately describes the textile’s behavior.The lab has even more grandiose ideas for their research, however. As Dimitriyev points out, knitters can effectively “program” their fabrics by manipulating the properties of each stitch. “Not only are these materials programmable,” he says, “they have an established coding language.” In fact, the conventions are so well-established that the vintage knitting machine in the Matsumoto lab takes instructions from punch cards, acting much like an early computer.Dimitriyev says that Markande’s attention to the smallest unit of knitted fabric, the knot, is like putting together the alphabet that will eventually lead to much higher-level functionality. Thinking forward to that functionality, Markande hopes that his work will help with the development of e-textiles , smart fabrics that can be made to absorb and store the kinetic energy generated by their wearers’ movements. Meanwhile, Dimitriyev is interested in knitters’ abilities to create highly specific geometries and elasticities just by varying the stitch pattern (in fact, some manufacturers are already starting down this path).

If you’ve ever been lucky enough to receive a handmade sweater as a gift, you likely spent more time than strictly necessary listening to its creator describing each of its virtues in detail:Although you may never have thought of your crafty relative as the engineering type, knitters actually spend a huge amount of time planning out the structure of their creations. After all, it isn’t easy to create a three-dimensional, highly structured object from a one-dimensional strand of yarn. Textile engineers contend with dozens of competing factors like strength, elasticity, texture, and cost. While these have traditionally been relegated to the fashion industry, Dr. Elisabetta Matsumoto’s lab at Georgia Tech sees them as a rich, hitherto unexplored field of physics.Michael Dimitriyev is a postdoctoral scholar who has been working with Matsumoto since 2017. Although his Ph.D. research focused on a different kind of material, polymer gels, he was drawn to the group when he realized that knitting and polymers are actually quite similar in some respects: while polymer gels are generally amorphous and knitted fabric is highly periodic, both are composed of a dense network of strands that gives rise to new and potentially surprising properties.For example, the yarn used in knitting isn’t typically stretchy; unless you pull really hard, it barely gives. And yet knitted fabric is often prized for its elasticity! There’s a reason that flexible garments like socks are almost exclusively knitted rather than woven. It’s emergent properties like these that fascinate Dimitriyev. “That’s not really from the properties of the yarn, that’s from the properties of the stitch,” he says. So, what is it about the knitted stitch that allows for such qualities to appear?Shashank Ganesh Markande, a fourth-year graduate student in the lab, focuses exclusively on the stitch-level properties of knitted fabric in the hopes of answering that question. He says that at its heart, what we call “knitting” is just the process of tying specific kinds of slip knots over and over again. “The way you entangle these things, and close them up, gives you an extra structure apart from the physics aspect of the yarn,” he explains. Although textile engineers have spent centuries figuring out how to manipulate these extra structures, he says it hasn’t really been formalized until now.Fortunately, a branch of mathematics known as knot theory has already been well-established for studying object like DNA and polymers. Now Markande is working to apply the framework to knitted materials. The basic idea is that knots can be characterized and studied based on how they are entangled in three-dimensional space. “The simplest loop would just be a circle,” otherwise known as an “unknot”, Markande explains. The next step up in complexity is the trefoil, which you may recognize if you have ever spent time untangling earbud cables.