Robert Lang was still working at his day job as a physicist in Silicon Valley when the bug wars broke out. Back in the early 1990s, the skirmishes were mostly local, the contestants mostly Japanese. "The first year, someone had a six-legged bug," he recalls. "The next year, it was a six-legged bug with antennae." A few years later, Lang joined the fray. For a formal bug-design challenge, held in 2004 on a muggy June in Manhattan, Lang and two competitors agreed to test themselves by creating a Eupatorus beetle. Eupatorus beetles are not simple insects. Sometimes called rhinoceros beetles, they have five horns of mixed length on their heads, tiny, vertical spurs at the joints of their six knees, and delicate, complicated toes. The contestants had to reproduce all these features on the Eupatorus, along with the rest of the beetle, out of a single uncut rectangle of paper. For the serious student of origami, making a Eupatorus is an extreme challenge.

In the dojo of the origami purist, there are only two rules: The folder may use just one sheet of square paper, and the paper cannot be cut or torn in any way. Following these rules to make a figure like a peace crane, with four basic features—a head, a tail, and two wings—is relatively easy, and origamists traditionally proceeded by trial and error, unfolding and refolding a piece of paper until it started to resemble, say, a swan. For hundreds of years, origami's most complex patterns topped out at 20 steps.

These days patterns requiring more than 100 steps are common. Some of that competitive acceleration is due to Lang, who transformed the art by writing a computer program that can generate the blueprint for ultracomplex origami sculptures. Even with digital assistance, figuring out the sequence of folds that will create a beetle and all its ornaments is a mathematical problem of staggering complexity. Still, the reigning champion of intricate origami is a 23-year-old Japanese savant named Satoshi Kamiya. Unaided by software, he recently produced what is considered the pinnacle of the field, an eight-inch-tall Eastern dragon with eyes, teeth, a curly tongue, sinuous whiskers, a barbed tail, and a thousand overlapping scales. The folding alone took 40 hours, spread out over several months.



Photograph by Garry McLeod

The four-inch praying mantis follows a crease pattern created with the help of TreeMaker, the program Lang wrote to speed up origami design.
"It's like an extreme sport," says Tom Hull, a mathematician at Merrimack College in North Andover, Massachusetts, and longtime origami enthusiast. The escalation in difficulty has grown so severe that OrigamiUSA has been forced to add a new difficulty rating to the four (simple, low intermediate, high intermediate, and complex) it has traditionally used. "People showing up to the complex sessions were getting blown to smithereens," Hull explains. "So now there's a new category: supercomplex."

 

Anatomy of an arthropod
Click on each fold pattern to see the paper bug it spawns.