Riffling through some papers on his desk, Lang pulls out the crease pattern that TreeMaker generated for a white-tailed deer. More than 200 equations factored into the algorithm. The resulting crease pattern—a network of lines running over a collage of circles joined by crenellated segments that Lang calls rivers—resembles a deer about as much as a cotton bush looks like a pair of jeans.

"Those are the ears," he says, indicating two small circles in opposite corners of the page. He taps some wavy lines that look like linked Japanese footbridges. "And that's the neck." He sees the uncomprehending look on my face and seems slightly embarrassed. "You just have to take it on faith, that when you collapse it down the right way, you'll get a leg."

Among origamists, TreeMaker is a revolutionary tool that saves hours formerly spent on folding and refolding just to get a simple animal's proportions right. Lang, however, is quick to point out that the program does not tell the artist what steps to take to get from the crease pattern to the final shape. An origamist is left to puzzle out the folding sequence, deciding upon the correct order and direction, out of literally millions of possible combinations, in which to make each crease.


Calculating this, as mathematicians like to say when facing a daunting challenge, is not trivial. Fold a square piece of paper diagonally, then fold it in half, and the result will be a small isosceles triangle. Switch the order of those folds—in half first, then diagonally—and you end up with a squashed pentagon.

The more folds a pattern has, the harder the problem of finding a folding sequence becomes. For one of his TreeMaker-guided designs—a life-size, anatomically correct Maine lobster—Lang was able to generate the crease pattern on the computer in just a few hours. Figuring out how to fold the 120-step pattern on a sheet of paper about 20 inches square took him almost two years.

"The mind-set to do advanced design is fragile," Lang says soberly. "You have to hold all these complex surfaces in your mind and figure out how they interact. If you're pushing the edge of the envelope on something like this, you need total concentration. Sometimes you'll have 5, 10, 20 creases, and you have to make them all happen at once. You need to develop an intuition about it."

To perfect their folding technique, Lang notes, rookies must also attend to details, like not creasing folds too sharply. "Do that and your piece will end up looking tatty. Plus, if there's a point where a lot of those creases come together, the paper can burst. It just puts too much strain on the fibers."

Lang gets many of the raw materials for his designs from Michael LaFosse, a master papermaker in Massachusetts. Among the exotic varieties are hairy paper, shiny paper, and paper so ethereal it seems to be made of fireplace ash. Nepalese lokta, a handmade fiber paper studded with tiny, grassy knots, is one of Lang's favorites—although he is also partial to abaca, a veiny material made from banana fiber. He almost always uses papers made from plant fibers other than wood pulp because they take a crease better and are less likely to rip under stress.

Origamists also toy with color, using papers that are irregularly mottled or that are one color on the front and another on the back. This aesthetic detail adds another layer of complexity to the crease pattern, which must then be designed so that the final animal—a bumblebee, perhaps, or a zebra—ends up with the right colors in the right places. In one famous example, origamist Neal Elias created a dancing couple from a single sheet of paper, folded so that the man was dressed entirely in black, the woman entirely in white. Lang recently made a lion out of fiber paper and folded it so that the paper's four original edges all ended up in the lion's mane. The edges were frayed, which made the mane authentically shaggy.

Although Lang is one of the world's top origami folders, he admits that his pole position is anything but secure. "The current generation is really remarkable," he says cheerfully. "Satoshi Kamiya, for instance, is just brilliant. He started as a child prodigy and came to the attention of the world origami community—the world community—by the time he was 15."

Unlike most elite origamists, who are often engineers or mathematicians, Kamiya is simply a genius. In Japan, where elementary origami is a popular pastime, Kamiya started folding with his mother when he was 2 years old. Early on, he showed a preternatural talent for visualizing complex geometric shapes. By age 10, he was designing his own sculptures. Last year he published a book, Works of Satoshi Kamiya: 1995–2003, which includes all his original designs. And he recently began making his own paper, which he engineered to be exceptionally thin and strong. "It was the only way he could make something so complicated," Tom Hull says. "The designs he's coming up with exceed the properties of ordinary paper."

For four years running, Kamiya has been crowned Origami TV Champion in a contest hosted by a Japanese game show. Some competitive events are almost maniacal in their intricacy. One year, he had to fold a fish underwater using waterproof paper. The next year, he was asked to fold animals that he first had to catch: a dog, plucked from a pen of 20 different breeds, and a fish scooped from a tank. The judges were fishermen and dog breeders; the winner folded the most animals whose breed was unmistakable.

Origami aficionados agree that Kamiya's most extraordinary sculpture is a dragon he created in 2004, at age 20. Coiled and rearing, the dragon has the lithe energy of a living snake, with overlapping scales, thornlike teeth, and tiny, grasping, clawed hands. Asked how he manages to create something so complicated without the help of a computer, Kamiya pauses to consider. "I see it finished," he says finally. "And then"—he stares off, as though visualizing the imaginary object—"I unfold it. In my mind. One piece at a time."

Lang and Kamiya meet often at exhibitions, but their methods remain distinct. Lang continues to tinker with TreeMaker, sticking with the computer-aided approach. Last year he devised a tricky algorithm to solve whether folds in a TreeMaker crease pattern were mountain or valley. Kamiya, too, continues to experiment, but he has no interest in learning to use TreeMaker. In halting English he says: "Right now, human way is better."

Meanwhile, the bug wars go on. At OrigamiUSA's annual convention in New York City this summer, Lang goes up against half a dozen other folders, including Kamiya, in a bid to make a sailing ship. Lang is mulling over a couple of approaches, but "frankly," he says, laughing, "I'd be putting my money on Satoshi Kamiya."