The Mind-Bending Artistry of Robert Lang

PAPER, NO SCISSORS, ROCK STAR: Origami artist Lang. Photo: Timothy Archibald

Over a muggy June weekend, more than 600 paper-folding enthusiasts from around the globe are gathered in New York for the annual Origami USA conference. The late-'50s-era classrooms at the Fashion Institute of Technology in Chelsea, where the conference is being held, are a study in beige, from the linoleum to the walls to the dressmakers' mannequins kibitzing in a corner. In one, 20 students ranging in age from 9 to mid-60s wait eagerly, packs of brightly colored paper spread out before them on the long, narrow tables. Their instructor for this course, Robert Lang, notes that the turnout is impressive, considering he didn't provide a sample of the model they'd be folding for the display downstairs in the great hall.

"This could have been a killer insect class," he says drolly.

Lang, MS '83, has certainly folded his share of creepy crawlies—a scorpion with stinger poised to strike, a Japanese "samurai helmet" beetle with formidable forked horn, even a pair of mating praying mantises—each from a single sheet of paper.

Prior to about the 1980s, origami arthropod designs were thought to be all but impossible. None of the known "bases," intermediate folded forms that might become any of a number of things, could produce both fat bodies and long, spindly appendages. Then came the so-called Bug Wars. Beginning in the 1990s, a handful of origami artists started applying mathematical design techniques developed by Lang and others to create ever more detailed and realistic models: insects with six legs, then eight, then extended wings, then forewings and hindwings, and so on.

An origami scorpion. Below it is a complex series of shapes representing its folds.STRIKING: A 7-inch-long scorpion folded from Korean hanji paper using a technique Lang developed called hex pleating. (Photo: Timothy Archibald; Crease pattern courtesy Robert J. Lang) 

The subject of this class, however, is not an insect, killer or otherwise, but a variation on a type of geometric origami called Sonobe. To the students, it doesn't really matter, though; it's Lang they're here to see. 

People who think of origami as simple paper playthings folded by schoolchildren may be surprised that there's such a thing as a professional origami artist, much less one who's a Caltech- and Stanford-educated engineer and physicist. A decade ago, Lang walked away from a successful career in lasers and optoelectronics to fold paper full time.

The moment he picks up a square of purple paper and begins creasing it in midair, long fingers moving at once with the precision of an engineer and the fluidity of an artist, it's clear he found his calling. Now widely regarded as one of the foremost practitioners of the modern art form, Lang has published more than 500 original origami designs. His work has been exhibited at the Museum of Modern Art in New York, the Carrousel du Louvre in Paris and the Nippon Museum of Origami in Kaga, Japan, among others. He also pioneered the use of math and computer science to design origami models so complex and intricate that it seems almost inconceivable that they were once a humble square of paper.

Lang's paper-folding prowess has brought him high-profile commissions—an American flag for a New York Times Magazine cover, for example, and origami characters and landscapes for Mitsubishi and McDonald's TV ads—and consulting work solving high-tech engineering problems using folding techniques. Art collectors can buy works of his existing designs priced roughly between $200 and $1,500; commissioned works usually run from $500 to $3,000.

When the session ends and classes spill into the hallway, Lang is greeted like a rock star. People ask him to pose for pictures and sign copies of his books and models; he gamely obliges. For the average origami enthusiast, the conference is a chance to meet their idols and fold side by side with them. For Lang, it's an opportunity to pay it forward.

Walking down seven flights of stairs (the elevators are out of service), he talks about his interest in folding as a kid growing up in Georgia in the 1960s. "There was no origami community, no conferences" at the time. When he was in his early teens, Lang got hold of the mailing address for Neal Elias, an insular yet innovative folder who pioneered several techniques, including box pleating. He wrote to Elias and the two started corresponding regularly. Lang says it made him feel connected and inspired him to create his own designs.

Paper-folding has a long history in Japan, where it was traditionally used in religious ceremonies and as part of etiquette rituals. (The word origami originally meant something close to the Greek diploma.) The earliest accounts of Japanese folding "for fun" date from the late 18th century. The designs were simple, abstract representations like the familiar flapping crane. A few inventive folders created new shapes by tinkering with the standard bases—bird, fish, frog, kite—resulting in a few hundred different designs.

An origami hawk elevated on a stand. Below it is a complex series of shapes representing its folds.SOARING: A red-tailed hawk with a 24-inch wingspan folded from Japanese kozo paper. (Photo: Timothy Archiald; Crease pattern courtesy Robert J. Lang) 

"You'd think that in 200 years, everything that could be made would have been," says Lang. But then along came Akira Yoshizawa (1911-2005), the "father of the modern origami." A self-taught phenom, Yoshizawa generated tens of thousands of new designs. His strict interpretation of the rules of "sosaku origami," creative paper-folding—one sheet of paper, no cuts—and naturalistic style elevated the folk craft to an art form. 

Perhaps more significant, Yoshizawa developed a visual language of dashed and dotted lines and arrows for conveying the direction and sequence of folds for his models. This notation system, which has been adopted with a few modifications as the standard worldwide, enabled the exchange of ideas, unhindered by language barriers, and opened the door for the spread of origami to the West.

The past 50 years have seen a dramatic increase not only in the number of unique origami designs, but also in their complexity. Prior to the 1950s, patterns had a maximum of about 30 steps and could be folded in a few minutes, even by a novice. Now, it's not uncommon for a pattern to have hundreds of steps and take several hours for an expert to fold.

What changed, Lang says, was the recognition of the underlying mathematics and application of an algorithmic approach to folding. If you unfold an origami model, you're left with a geometric pattern of crease marks on the paper. People started to figure out that there were mathematical rules that governed how crease patterns related to finished shapes.

Lang was among the first to formalize these ideas and lay them out as a method other people could follow. "People innovating in the '60s and '70s were following mental algorithms that they knew were going to work," he says. "They just couldn't tell you why." The power of these techniques has changed the way people approach origami design from "experimentation guided by intuition" to what Lang cheekily refers to as the "era of intelligent design."

Step-by-step instructions for folding Lang's take on the Tree (PDF)

From a young age Lang also loved math, and when he got to college he figured that's what he'd study. But the first "pure math" courses he took as an undergrad at Caltech weren't what he expected. Instead he gravitated toward electrical engineering because he "liked building things." After taking a lab class from one of the inventors of the argon ion laser, he became interested in optics. At the same time, he continued to "push the envelope" with origami, "trying to do things that hadn't been done before or that even seemed like maybe they couldn't be done."

He began to see connections between origami and math. "One of the things you learn in a technical education—physics or engineering—is that, you enter a field, you try to build a mathematical model of the phenomena in that field. And once you've got a mathematical model you can use the tools of math to exercise that model and sort of learn stuff for free," he says. "Origami felt the same. It was clear there were underlying natural laws that limit what you can and can't do. And if I could identify what those laws were explicitly, then I could use mathematical tools to make the things I really wanted to make."

Two hands fold paper into a triangle on a desk beside a calculator.HANDS OF A MASTER: Designed with the aid of mathematical and computational tools, Lang's creations are ultimately brought to life, fold by painstaking fold. (Photo: Timothy Archibald) 

At Stanford in the early '80s, Lang continued to take a "heavy mix of optics" as part of his EE coursework while working a day and a half each week at IBM in San Jose. He also started writing and sketching diagrams for his first book, which was published in 1988 as the Complete Book of Origami. "A terrible title," he concedes, because "it's not nearly complete." He's since published a dozen books containing folding instructions for more than 170 figures. 

After Stanford he returned to Caltech for a doctorate in applied physics. There he met Diane Davis, and they married shortly after he graduated. She accompanied him to Germany, where he had accepted a postdoc position working on semiconductor lasers. Living in Ludwigsburg, near the famed Black Forest, inspired one of Lang's most recognizable creations: a life-size paper cuckoo clock featuring a deer head with antlers; a bird perched on an extended platform; a face with hour and minute hands; pinecone-shaped weights; and a pendulum. It took three months to design and six hours to fold from a 1-by-10-foot piece of paper. It was the most complex object anyone had ever folded from a single sheet, and it established Lang's reputation in technical origami circles.

Around this time, Lang says, he started wanting to write a different kind of origami book. It would do more than give "recipes" for folding a couple dozen models; it would teach people how to design any model they wanted. "How do I get six legs and not eight and not four?" he says. "By that time I had developed lots of ways to do just that, to get exactly six. And if you wanted some of them to be this long and some of them that long you could do that, too."

For the next 14 years, while building a successful career as a laser physicist first at NASA's Jet Propulsion Laboratory in Pasadena, Calif., and then for Spectra Diode Labs/JDS Uniphase of San Jose, he tried to write but made little headway. With recipe-type books, he says, he could work in snippets of time, leave off and come back later. But for the design book, he needed "a coherent picture, a narrative arc," and he found he couldn't do that piecemeal. The only way to write the book he wanted was to do it full time. "It was like the scene in The Matrix: Do you take the red pill or do you take the blue pill?"

In 2001, Lang decided to go for it. Origami Design Secrets: Mathematical Methods for an Ancient Art took a year and a half to write and was published in 2003. In it, Lang describes how each "flap"—which might become a wing or a leg or a tail in the finished model—takes a circle, or part of one. (The circle's radius determines the length of the flap.) The arrangement, or "packing," of these partial circles within the square of paper forms the basis for the crease pattern.

"A person can, on a piece of paper, draw circles and see how they pack and then sketch the lines between them. And that gives you the crease pattern and from that you can start folding," Lang says. "The approach I took when I wrote Design Secrets emphasized that scheme because that's what most people have accessible to them: pencil, paper and those ideas."

A pathbreaking book, it will be published in an updated edition in August. Reflecting on its impact, Lang says, "Twenty years ago you could probably name the 10 origami designers out there. Now, here at this convention you've probably got 50 designers represented. And I'd like to think—and I've heard this from some—that a lot of them are designing because they got Origami Design Secrets."

His peers are less circumspect. "His books are incredibly influential," says Tom Hull, an associate professor at Western New England College and expert in the mathematics of paper folding. "When people think of really complex technical origami, they think of Robert Lang." Even among mathematicians, Hull adds, Lang has a reputation as "someone who does the math right."

Lang's design techniques have spurred talented young folders like MIT grad Brian Chan to even greater heights of complexity. "Before his book," Chan says, "there was a lot of discussion in Japan about various technical aspects of origami design, but no easily accessible resource to aid aspiring designers of origami. Lang's theories of 'circle packing' and 'molecules' in origami are what got me and many other complex folders started in designing what would become some of the most complex origami in the world."

Of course, the technical proficiency that goes into folding a piece does not, in itself, make it art. "By using the design tools," Lang says, "you don't need to devote energy to that part of it, so it does free you up to devote most of your energies to the creating of life." John Montroll, a dai sensei (grand master) of origami and prolific author with whom Lang has collaborated on several books, says that he's been most influenced by Lang's work "toward a deeper understanding of internal workings" of origami models. "Robert brings a high level of both the technical aspect and the artistry that had not been there before."

This can be seen especially in Lang's models that draw inspiration from the natural world. "The folds that I spend the most time and effort on are the ones that most move me when I see the real thing," he says. "A bird is wings, a head, a tail and, if you want to be fancy, feet, and that's it. But the emotional response I get when I see a real soaring red-tailed hawk, that's what I want to capture in the fold. And I keep working and I think each time I do a new raptor I get a little better at capturing that emotion."

This method of designing is distinctly different from the stepwise way people historically developed new origami models. When you fold from a crease pattern, there's no guarantee that a neat sequence of folds exists that will take you from flat sheet to finished object. In most cases, in fact, all of the creases—or a very large number of them—have to come together at once. In origami this is known as "the collapse," and it can take hours.

There's an analog for this in life, where disparate events, spread across years, come together to reveal the path forward. It goes by a nicer name, though: serendipity.

About a year before Lang decided to leave the laser world to become a full-time origamist, he got a call from a researcher at Lawrence Livermore National Laboratory who was looking for a way to fold a football-field-sized lens into a compact package that could be launched into space. The researcher had found a paper Lang wrote back in 1996 for a computational geometry conference; he had no way of knowing that the paper's author lived only five miles down the road in Pleasanton, Calif. What's more, the symposium for which Lang submitted the paper—his first in computer science—was very competitive. What tipped the balance in his favor, Lang believes, was that as a graduate student, one of the committee members had published an origami journal in which Lang's work appeared.

An origami deer and a a large grid of lines and circles representing its folds.STAGGERING: An 8-inch-tall mule deer designed using TreeMaker, a computer program Lang created. (Photo: Timothy Archibald; Crease pattern courtesy Robert J. Lang) 

Lang came up with a radially symmetrical design to fold a five-meter prototype of the lens for the Eyeglass space telescope down into a cylinder four feet in diameter by two feet tall (not unlike the way a compact umbrella collapses). And though the telescope never did make it into space, Lang's work for LLNL led to other consulting gigs: for NASA on a solar shroud; for a medical device manufacturer on a mesh heart-support implant; for an automotive engineering firm on airbag computer simulations; for a cell phone maker wanting to get the antenna to fit inside the phone body. 

Other fortuitous wrinkles led Lang and his wife to their current home in Alamo, Calif., situated between Los Trampas Regional Wilderness and Mount Diablo State Park, and complete with a detached artist's studio. "I didn't even dare to dream about something like that. I was thinking I'd rent office space in some dingy little alleyway somewhere," he says.

Surrounded by fauna literally in his own backyard, Lang works on refining his raptors and building a better beetle. Among his latest works in progress, an arboreal click beetle with fringed antennae is, he says "one of the hardest things I've folded to date." Killer, indeed.

Greta Lorge, ’97, is a Bay Area writer and editor.