Most people think origami means making paper cranes. But a former laser physicist is combining origami with technology to not only create beautiful pieces of art, but to design better air bags and medical devices as well. This ScienCentral News video has more.
Folding Mathematics
Robert Lang had a successful career as a laser physicist working at Caltech and several private companies in California. But his lifelong hobby of origami eventually won out, and now he's a full-time origami artist.
Origami is the ancient art of paper folding, and the most common style is folding a single uncut piece of paper. But Lang says that whether you're folding a piece of paper or engineering an air bag, it's all about the math. "When a person looks at origami, they're seeing art, but in many cases it's art that was enabled by mathematics," he says.
While he says that many origami artists have no mathematical background, his work in computational origami and origami mathematics has ratcheted up the competition in the field. Origami artists traditionally fold, unfold, then fold again to create new designs. Lang created a computer program to invent new, complex patterns and calculate precisely where the paper should be folded. "I realized that I could use the same math and ultimately computer tools to describe the process of making an origami model in the same way that I used math and computer tools to describe a laser," he says.
The computer program, called TreeMaker, uses hundreds of mathematical algorithms to calculate crease lines in origami paper. "It was the first program that could design an origami shape that was more complicated than what a human being could design working with pencil and paper," he says. The program does better with stick-figures, he says, meaning that thin figures like insects are easier to make than rounded creatures like an elephant. TreeMaker is available for free online.
While Lang's creations have been shown in galleries internationally, he's also commissioned to do projects for organizations with folding problems. "And while you use these tools to create art," he says, "you can also use these tools to create objects that have practical purposes."
Lang has worked with Lawrence Livermore National Laboratory on their plans to send a large lens into space. "So picture a lens the size of a football field," he says, "and it has to be collapsed down to fit inside of a rocketship. That's the only way you can get it to space."
He says that origami's principles can be used for anything that folds, from better packaging to expandable medical implants, like stents that prop open clogged arteries. "Any person walking around the street might have a little bit of origami somewhere inside their body," he says. Even cell phone manufacturers were looking to origami to design better antennas that fit inside small handsets.
Origami piece "Allosaurus Skeleton, opus 326" image: Robert Lang
Lang says that origami shares some traits with architecture, where an understanding of the math can bring the field to a new level. "If you look at a beautiful monument, you're looking at a piece of art," he says. "As people learn to build more and more complicated structures, that enables them to build more and more beautiful pieces of architecture." He says that as origami artists learn more about the math behind origami, it expands the types of creations that they can make.
While his program creates the crease lines for origami pieces, it can't give step-by-step directions to get to the finished product. "TreeMaker gives you all of the creases, but it doesn't tell you the order in which the creases need to be made," he says.
Even with the computer, it has still taken as long as two years for Lang to figure out how to fold some of his pieces step-by-step. Sometimes he has to crease all the lines first, then try to bring it all together at once. "You might have more than 100 folds that have to be manipulated, and you only have 10 fingers to do the manipulations," he says. That's where state of the art technology needs some old-fashioned handiwork.
Lang's paper on "A Computational Algorithm for Origami Design," was published in the 1996 Proceedings of the 12th Annual Symposium on Computational Geometry and his work was featured in the July 2006 Discover magazine. His TreeMaker computer program was self-funded.
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