At its core, origami consists of just two folds, mountain and valley. A mountain fold is what you get if you crease a piece of paper so that it stands up like a pup tent. A valley fold is the same thing turned upside down. Valley folding each corner of a square so that they meet in the center creates something that looks a bit like a cheese blintz and is therefore known as a blintz fold. Beyond these two basic folds, the grammar of origami proliferates rapidly. It's possible to blintz a petal fold, or double blintz it. Likewise, combining a series of squash and petal folds yields a frog base—one of the four traditional bases (called kite, fish, bird, and frog) from which many traditional origami animals are fashioned.

"All the parts of a base are linked together and can't be altered without affecting the rest of the paper, so that's the part you have to calculate just right," Lang says. A base with four flaps is relatively easy to make. Each flap is formed from one of the corners of the square. Making a base with 17 flaps of the right size and in the right places—what you'd need to create Lang's flying rhinoceros beetle—is exponentially more difficult. "Figuring out how to make good legs was all people did for years," Tom Hull says. "Doing a six-legged beetle was a big, big deal."

Lang resisted the challenge for a while. He spent most of the past two decades working as a laser physicist—first at Caltech, then later for private firms in Silicon Valley—and devoted his off-hours to origami. By 2002, his interest in origami won out. He quit his job and began folding paper for a living.



Photograph by Garry McLeod

A seven-inch origami insect—a winged walking stick—is among Robert Lang's newest creations.
Since then, he has created everything from a ruby-throated hummingbird to a full-scale human (commissioned for a German trade show). The jobs are sometimes banal—there's a lot of demand for cardboard fast-food containers that change shape—but every now and then Lang gets tapped for a more challenging project. He has been asked to simulate the folds of a car's air bag when packed into a steering column and to design a telescope lens that could be shot into space packed into a nine-foot cylinder and then unfurled to the size of a football field. He also recently consulted on the development of an origami-inspired medical implant, which he can't talk about other than to say that it was "big, permanent, and what keeps the person alive." Origami also turns out to be useful for biological problems, such as determining how proteins fold in the body.

Over the past 15 years, Lang has been perfecting a program he wrote called TreeMaker, which can render a stick-figure sketch into a crease pattern—the web of lines that would be left if a finished piece of origami were unfolded and then smoothed. The software converts the sketch into a set of equations that calculate how the appendages of a complex animal form, like a deer, should be distributed on the paper in a way that ensures they will neatly emerge during folding without leaving excess paper or creating areas so wadded up that they can't be folded.