Origami may be about creating beautiful objects from flat pieces of paper – but, as the career of American origamist Robert J. Lang shows, it’s increasingly about maths, engineering, medicine and space
What links space telescopes to atomic legends? Heart surgery to crumpling cars? Printable robots to houses that can reconfigure themselves? Or paper cranes to curved, plant-like sculptures exhibited at New York’s MoMA? The answer, perhaps surprisingly, is origami – now a respected branch of mathematics, geometry, engineering and art.
“Until the late 20th century, with a few notable exceptions, origami was mostly seen purely as a traditional Japanese craft,” says Robert J. Lang, a world-renowned American origami artist who builds origami computer programmes, hosts TED Talks and designed the folding pattern for satellite telescopes. “But then, in the 1990s, we started really looking at the mathematics behind it all, and started seeing these almost infinite possibilities. It was a revolution of sorts.”
The history of origami (the word comes from the Japanese for “folding paper”) is a diverse one. In Japan, origami butterflies marked Shinto weddings as early as the 8th century, and making paper cranes, hats and boats has been a Japanese pastime for more than 400 years. Across the East China Sea, the Chinese have burned folded representations of gold nuggets at traditional funerals since the Song dynasty (960-1279).
Led by the Japanese, magicians began to use origami in the late 19th and early 20th centuries, and in 1922 Harry Houdini even wrote a book about performing with paper. (Paper-folding is thought to have developed separately in Europe; by 1847, German educator Friedrich Fröbel introduced it to his revolutionary new early-childhood education programme, kindergarten.)
But the real godfather of modern origami was Akira Yoshizawa, a former door-to-door fish salesman who created more than 50,000 models in his 94 years, pioneered wet-folding and whose work has inspired people in Japan and the West to develop new methods of design (see sidebar).
This was the world that Lang started exploring as a precocious six-year-old in late ’60s Atlanta, Georgia, making his first Japanese frog, talking crow and flapping bird. “At ten or 11, I’d folded everything in the basic books I had, when my parents bought me books by Isao Honda and Robert Harbin. That opened the floodgates, and by 11 I was starting to do original designs. I started off turning crows into eagles and then the modifications got bigger and bigger.”
Lang started to see design patterns, and had designed everything from President Jimmy Carter to Darth Vader and TV pig Arnold Ziffel, when he came to something that mathematicians had been exploring since the 1940s, albeit largely in isolation – the link between mathematics and origami. “It really hit me at college that if I could figure out how to describe origami mathematically, it could help with design problems,” he says.
By 1988, he had completed an electrical engineering course and a PhD in applied physics, and was working at NASA’s Jet Propulsion Laboratory in Pasadena, California. After a trip to Germany’s Black Forest with his wife, he created a sensation in the origami community with a life-size cuckoo clock, which had taken three months to design and six hours to fold.
But he was just getting started, as was a new wave of origami. Few have heard of the “Insect Wars”, but if you were a high-level origami artist in the early 1990s it was a big deal. The challenge was that, until then, origami designs could make shapes that were, in Lang’s words, “blob-like or amorphous”. The skinny legs and tentacles of insects were thought almost impossible.
But in the late 1980s, Lang – along with a group of origami experts including Japan’s Toshiyuki Meguro – had started to pioneer a new origami design technique called circle-river packing, which uses geometric principles to create an almost infinite number of designs.
“In the 1970s, they couldn’t figure out how to make a spider,” Lang says. “But with the outgrowth of new techniques you could make a millipede, or really any creature you wanted. People ask me what changed, and the simple answer is math. It seems counter-intuitive that you learn how to depict an animal using mathematical principles, but that’s how it happened.”
As his emperor scorpions and Hercules beetles were sent around the world, particularly to meetings in Japan – “We were constantly trying to one-up each other” – in 1990 Lang went a step further than his peers, putting his mathematical findings into a computer program called Treemaker. You can insert stick-figure shapes into Treemaker, and have them turned into intricate folding patterns. He has been refining it ever since.
Treemaker and circle-packing went a long way to an explosion in artistic origami. Satoshi Kamiya, a young Japanese origami master, created Ryujin 3.5, an elaborate dragon with intricate scales, feelers, claws and horns, which took 40 hours of painstaking folding. But the Bug Wars also changed the game for origami as a science. “It’s been a snowball effect,” says Lang. “As the mathematics have become more powerful, the connection between engineering and origami has grown exponentially over the past 20 years.”
By 2001, he was able to leave his job at JDS Uniphase, which supplied components to computer companies, and become a full-time origamist. A lot of his job revolves around art – on his website, you can see more than 650 sculptures, from scores of beetle species to complex mathematical shapes and an origami pteranodon with a 2m wingspan that was commissioned by Montreal’s McGill University – but it also increasingly has a scientific purpose.
He has been commissioned to create sterilised pouches for medical instruments, which can be opened and closed without desterilisation occurring; and heart supports that can be injected via a thin tube before spreading out to support hearts. He’s worked on airbags and mobile phone antennae, and on various deployables in space, including a telescope with a 100m lens, which could be folded into a rocket.
“Origami touches on so many things,” says Lang. “The curved carbon fibre skins of airplanes are made using origami principles, and folding patterns are used in cars so that, if they crash, they crumple smoothly and cleanly.”
Certainly, this craft – long associated with Japanese paper cranes – has grown up. “Ever since we had the first Origami Science and Technology conference in 1989, it’s definitely been looked at differently. At its core, it’s still that same process – folding something flat to make something three-dimensional – but it’s so much more than a craft now. It’s art, science and mathematics in one place, and the possibilities are infinite. Origami really can change the world.”