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Paper Shapers

altLate UCSC professor and origami pioneer honored with eye-catching exhibit

Few would see the beauty of an algorithm scribbled onto a page, but when that same math is folded into the paper, the result is something that could not have been created by the imagination alone; it exists thanks to the fortuitous whimsy of mathematics.

At “Origami: Art + Mathematics,” an exhibit which opens on April 8 and will run through June 16 at the Eloise Pickard Smith Gallery at UC Santa Cruz, the art on display might be hard to believe, much less comprehend. The exhibit honors the late David A. Huffman, UCSC professor of information science and pioneer of mathematical origami, whose rarely seen artwork will be featured alongside work from multiple renowned origami artists.

“You will see things folded that you would not believe could exist,” says Robert J. Lang, a physicist and origami master, who will be presenting a pair of lectures in addition to contributing some of his own work to the exhibit. While the two lectures have a different focus, Lang says “they’re both about the connections between origami, math, science, and technology.”

One of the lectures will concentrate on some of the underlying mathematical laws of origami, in addition to providing examples of how the algorithms and theorems of origami design have elucidated longstanding mathematical questions and answered practical engineering problems. The other lecture will be of a less technical nature; Lang will be joined by Erik Demaine, who will also be giving another lecture and contributing artwork to the exhibit.

altLang, who started practicing origami at the age of 6, says his motivation for practicing the art form has varied over the years. “When I started, I think origami was just a way of making toys, and I didn’t need much in the way of raw materials, because all you need is a sheet of paper,” he says. “But as I continued with it, I became attracted by this idea of creating something from almost nothing. … That concept eventually became the reason I stuck with it and tried to develop it further.”

Demaine, a professor at MIT, began exploring origami when he was a graduate student interested in computational geometry. “I got hooked pretty quickly,” he admits. “Paper just has a really neat geometry. It has very simple rules; you’re just not allowed to stretch or tear the material—what can you make? It’s pretty tantalizing and also quite deep mathematically; it’s quite tricky to figure out the answers to these problems.”

As one might expect, the artistic process from planning to execution of any given piece is an extensive one. Lang says the process varies depending on whether the subject matter is representational—which includes most of his work in the exhibition—or geometric, which is usually triggered by a mathematical idea or concept.

altFor the former, which attempts to convey the essence of a subject, Lang starts by deciding what features of the subject are important to emphasize and represent, and which ones can be left out. “Then it transitions to a more mathematical development where I translate those artistic concepts into a mathematical description, and that allows me to use the tools of mathematics to actually carry out the design,” he says. “So instead of talking about, say, arms and legs and wings, I’ve translated those into geometric shapes like circles and rectangles and hexagons that represent those features, and I can put those geometric shapes together to make a plan for how to fold the whole shape.”

After executing the folds based on that plan, Lang transitions back into a more artistic and intuitive development. “As I’m actually doing the folding, I’m seeing resemblances between the forms that the paper’s taking on and the shapes that represent the subject,” he says. “Acting on those intuitive notions to adjust the shaping, and to add folds, or to thin flaps, it’s more like a sculptural form, where a sculptural artist might just move clay around from here to there. In this case you can’t pull paper off from one place to another, but you can alter its shape through folds.”

Demaine, whose father—and frequent collaborator—has a background in visual arts, describes the process of origami as a communication with the canvas. “We’re sort of having a conversation with the piece of paper,” he says. “We put in these creases and it wants to live in a particular kind of form, and then we’re manipulating those pieces so that they interact with each other in some way, and when we let go, they kind of relax to their natural equilibrium. There’s a lot of back and forth between us and the paper, until we are in a happy balance.”

As suggested by the name of the exhibit, much of the featured work is a union between art and mathematics, which should be eye-opening for those who do not normally equate the unbreakable austerity of mathematics with creativity—or indeed, beauty. Lang, however, views mathematics as an essential tool in his artistic arsenal. “It’s fair to point out that there are artists who use little or no math, who work almost entirely within an intuitive milieu,” he says. “But for me, I find that if I bring mathematics into it, I can accomplish a lot more artistically than if I didn’t.”

While the rules of origami prohibit much in the way of literal flexibility, the evolution of the medium has an appealing elasticity; even though it is a centuries-old art form, it continues to transform in new ways. “Origami as an art form has really changed a lot over the last couple of decades because of the growing mathematical understanding of how paper folds,” says Demaine. “It gives artists the power to be more expressive. Every year I feel like it evolves a lot and you see pieces that you wouldn’t really imagine are possible.”

altHuffman was certainly at the forefront of origami’s modern evolution, particularly as a pioneer of curved-crease folding (folding along a curve instead of a straight line), and his legacy has only continued to grow since his passing in 1999. “He made a lot of amazing sculpture and a lot of written notes about what he was discovering and designing using mathematical tools,” says Demaine.

Regarding Huffman’s work in curved-crease folding, Lang says, “It was very unlike what people had been doing in the origami world; people realized this was something new, and the world of origami could benefit enormously from knowing and using it. He had described mathematics that provides a way for modern paper artists to learn from what he did.”

“Origami: Art + Mathematics” opens April 8 and runs through June 16, at Eloise Pickard Smith Gallery, Cowell College, UCSC, 1156 High St., Santa Cruz. The Artists’ reception takes place from 12:30-6 p.m. on Sunday, April 8. For reception details, visit cowell.ucsc.edu/smith-gallery/exhibition-schedule/current.html. Free Admission. For more information and gallery hours, call 459-2953.

Photo 1 CREDIT: Matthew Mulbry

Photos 2 & 4 CREDIT: Art by David A. Huffman, Photo by Tony Grant.

Photo 3 CREDIT: Robert Lang.

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written by JanetG, April 24, 2012
Are there any patterns/instructions available for these?

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