On the ground floor of PennDesign’s Meyerson Hall, in the exhibit space in the back-right corner, a wonderful world of folded, cut, colorful construction is on display. Some items look like doilies, others like children’s connector toys. One looks uncannily like a paper version of the Death Star.
The work is called kirigami, and it belongs to artist Mike Tanis. But the purpose of many of the structures goes far deeper than just visual enjoyment, into the realm of theoretical physics. That’s because Tanis is the artist-in-residence in the lab of Randall Kamien, a professor in the Department of Physics and Astronomy whose research focuses on defects in crystals.
Kamien has been using kirigami—which literally means “cut paper”—since 2013 to come up with a set of rules that guide how such defects work, and in January 2015, Tanis saw an article about the Kamien group. Tanis had been playing around with origami and kirigami himself and decided to reach out. Initial conversations turned into informal bi-weekly meetings with Kamien and members of his team, like former postdoc Toen Castle, and eventually they formalized the set-up, giving Tanis an office and free reign to fold and cut as he saw fit.
Ultimately, the goal of the collaboration is to apply what the team creates to real-world scenarios. It’s already happening with surgeons from the Perelman School of Medicine, who have begun to use the kirigami algorithm Kamien and Tanis built in reconstructive breast surgery. And there are applications for architecture and design, too.
“Having an artist-in-residence is totally mind-blowing,” says Kamien, the Vicki and William Abrams Professor in the Natural Sciences. “It’s like when I play chess. I know all the rules, and in principle, I could figure out what you’re going to do, but I’m not very good at chess. Then there are the chess geniuses who can see deep into the game. Mike is like that. Mike takes the rules—the same rules that everybody knows for kirigami, just like everybody knows the rules for chess—and he then turns them into something so much bigger, so much more intricate than what we could possibly have imagined.”
The art of kirigami
Truly understanding how cutting and folding paper might lead to useful tools for doctors and architects requires understanding kirigami as a practice. If it’s hard to visualize, imagine one of those 3-D pop-up birthday cards. Closed, it lays flat; open, it reveals a house or balloons or some other three-dimensional paper structure.
Or think about origami. A flat piece of paper gets folded and folded until a crane or a box takes shape. Kirigami is similar, in that it begins with folds, but it differs in that it also includes cutting and, in some cases, reattaching. “We’re actually changing the curvature of a sheet,” Tanis explains. Unlike origami, “it can’t be folded flat once it’s assembled, which gives it more structure and properties you wouldn’t get from just a folded sheet or even a structure made in a mold.”
It’s also a very rational process, Kamien explains. “We can decide ahead of time what’s going to happen,” he says. “If you’ve ever done origami and you start following the instructions, you’re hard-pressed to see how a bird is going to arise out of the sets of folds. Here, it’s much more direct. You want to make something go up? We figure out how to make something go up. You want to make something go down, we can make it go down. We’re just following a small set of rules.”
Kamien gives an example to clarify further: Consider attaching an old, five-story building with high ceilings to a newer, six-story building with low ceilings. The top floors match up—the fifth floor of the old building attaches to the sixth floor of the new building—so that the two blend. The ground floors connect, too. Given those facts, how do the other floors line up? Usually, he explains, by a half floor in the new building, typically called the mezzanine. Except at the end of that mezzanine, the buildings look fine, with one floor on top of another, staircases, elevators, etc. But the place where the mezzanine ends is called a “defect.”
The same idea applies to crystal defects, which are well-understood by science. Crystals are made up of ordered stacks, and when those stacks mis-stack just a little, that causes a defect. It’s like a pattern that alternates between red and blue until accidentally, an extra blue gets thrown in, leading to two blues in a row.
“We wanted to take the mathematics that describe the crystal defects and use that to construct rules to fold things into the shapes we wanted,” Kamien says. “We actually introduce cuts and throw stuff out. It’s like you had a perfect crystal and somebody came along and took some layers out of it, in the middle, not the whole layers, just some of the layers. From far away the crystal looks fine, but as you get closer, you realize there’s something missing.”
A unique partnership
Though Kamien and Tanis have each been thinking about kirigami separately for some time, their collaboration is still developing. And although Tanis is formally the artist-in-residence, and has been for three years, that’s just about the only formalized part of the arrangement. Intentionally so, it seems. Tanis doesn’t have a scientific background and he thinks like an artist—both of which make his perspective so valuable to the Kamien group.
For Tanis, kirigami just clicked. He has no formal training in it, learning by trial and error. “I wasn’t interested in doing patterns out of a book, animals, or representational kind of sculpture,” he says. “I was into structure and especially the mechanics of it. I quickly got obsessed with it and tried to make my own patterns.”
Today, he plays around with triangles, squares, and hexagons—the basic geometric building blocks—using paper, plastic, Q-tips, and fishing line. He tests out different folding and cutting patterns. He builds moveable models that change shape if you throw them in the air. His office has shelves filled with pink and orange and white and clear projects, some completed and acting as reference material, others in progress.
In general, Tanis doesn’t aim to solve any particular problem through each piece he creates. Rather, he designs something, then brings it to Kamien, at which point they discuss how it has potentially broadened their understanding of a scientific concept, say, or how it might be applicable to real-world practices.
“Mike basically has a license to be awesome,” Kamien says, “and he constantly brings us great stuff.”
Practical applications
Some of their conversations have already turned into fruitful partnerships, like with surgeons in the Perelman School of Medicine who do reconstructive surgery for breast cancer patients.
Whether reconstruction occurs using implants or fat and skin from a patient, it typically requires something to hold the implant in place. Sometimes this is made from an absorbable mesh, but often it’s made from a skin graft. To mimic the breast form the body makes naturally, surgeons need to cut and sew this artificial skin to make the sling. Now, using a pattern that Kamien and Tanis developed, there’s no guesswork within that process.
“Working with the surgeons, we’ve actually come up with a set of algorithms and tools so that they could take transplanted skin, cut it just the right way, and use that as a pouch, which eventually becomes absorbed into the body,” Kamien says. “Surgeons have already been putting artificial skin into people and cutting them and sewing them together. Kirigami gives them this algorithm to do it in a way where they get the pattern they want.”
And of course, there are design possibilities, too. Hence the exhibit in one of the buildings at PennDesign. The room is small, so it’s easy to miss. However, several of Tanis’ colorful pieces sit on shelves outside, near the little café and the building’s main atrium. They catch your eye, even if you’re not looking for them. “The idea is to get this out to architects to see if they can do something with our mechanisms, our patterns, on a much larger scale,” Tanis says. “Kirigami is meant to be a general, scalable process that you can apply to things that may not have been feasible before.”
It’s big thinking for objects that are, essentially, glorified pieces of paper and plastic. But given the hundreds of structures Tanis has already created and the ingenuity of his collaboration with Kamien, they seem to be onto something, using theoretical physics and kirigami to shape innovations in medicine, design, and much more.
Randall Kamien is the Vicki and William Abrams Professor in the Natural Sciences in the Department of Physics & Astronomy in the School of Arts and Sciences.
Mike Tanis is the artist-in-residence with the Kamien lab.
Homepage photo: Artist-in-residence Mike Tanis uses colored Q-tips and fishing line to create kirigami structures like the colorful shapes seen here, built using basic geometric shapes like triangles, squares, and hexagons.
