Computational Origami

Ancient art finds industrial, medical uses.

Robert Lang, a laser physicist and origami artist for more than 30 years, continues to be amazed at the potential applications of the centuries-old art of paper folding. "You would think that there is not much you can do with origami as an art form that has not been already figured out," he says.

But, Lang adds, origami artists continue to "demonstrate new structures and realize new levels of beauty," a statement well supported by his own origami renderings of subjects such as cows, fish, blue herons and owls.

Origami was purely a hobby for Lang until he decided to apply the kind of mathematical modeling he used in laser physics to paper folding.

Lang, who is based in Alamo, Calif., now considers himself a full-time artist. He says computational origami helped him automate the process by which he determined how to make the precise kinds of folds needed to produce a multilegged insect and its antennae.

After he did that, he realized that the theory and equations he developed to make better origami figures could also be applied to engineering problems in which a large surface needs to be folded to fit into a flat space without cutting.

Today, while concentrating on his art, Lang also works as an industrial consultant, applying his computational origami expertise to the design of a range of products, including consumer electronics and medical equipment.

From Birds to Air Bags

EASi Engineering GmbH in Alzenau, Germany, asked Lang to help determine how to squeeze a very large object -- an automobile air bag -- into a tiny compartment inside a steering wheel. Lang had already developed algorithms to flatten a set of polygons, and he applied them to a computer simulation of how to flatten the 3-D polyhedron shape of an inflated air bag. This process saved time and eliminated the expensive requirement of crashing real cars to determine if an air-bag design would really work, Lang says.

The air-bag design was based on an algorithm Lang calls the "universal molecule," which flattens a set of polygons so their edges remain aligned to one another.

Lang sees a definite future for computational origami in engineering and design work, but he acknowledges that the field is relatively esoteric and requires artistic as well as computational, mathematical and engineering skills.

"You have to be able to fold paper" before proceeding to computational origami, he says.

Lang developed software called TreeMaker that runs on Apple Macintosh computers and helps automate origami design. The program, which Lang said can be mastered by a high school student, helps users figure out how to fold a square into a number shapes. A user outlines a figure on the TreeMaker screen, and the software determines the number of flaps required to make that particular shape.

If users want to create advanced designs (such as that of an air bag), they can can download additional algorithms from the Treemaker Web site (

But Lang says only 100 or so people have downloaded the software, and only about five or 10 are using it, another indication that the field of computational origami is still in its early stages.

Bad Folds

Erik Demaine, a 22-year-old professor of electrical engineering and computer science at MIT, started folding paper at age 6 and developed that hobby into the study of the mathematics of folded forms.

Demaine now studies folds in proteins, the basic building blocks of life. He believes that computational origami could fight diseases that are currently incurable, such as mad cow disease, which are caused by proteins that have what he calls "bad folds."

Demaine, a 2003 winner of a MacArthur Foundation Fellowship -- commonly known as "genius" grant -- calls protein folding his "main area of interest" and says he plans to apply what he learned from paper folding to figure out why some proteins fold into a useful shape and others do not. That research could eventually lead to the design of custom proteins that fight disease. The custom proteins could then be unleashed to destroy "bad" proteins.

Ajay Royyuru, manager of the computational center at IBM Research in Yorktown, N.Y., agrees that determining the way various proteins twist and fold could help provide cures for diseases such as Alzheimer's and cystic fibrosis.

Computational origami could help scientists crack some basic secrets of protein structure and sequence, Royyuru says. The technology could help scientists determine why a protein falls into a specific shape "and why that shape and nothing else." High-speed computers can be used to develop "fold recognition" software and help simulate folding patterns, Royyuru says.

But determining what he refers to as "correct" and "incorrect" protein folds by modeling them with computational origami is a daunting task, he says, requiring computers two to three times more powerful than the most powerful supercomputer in existence.

That power can be delivered only by a computer operating at a quadrillion operations per second (1 petaflop, or 1,000 teraflops), and IBM is developing such a computer as part of its Blue Gene project. IBM says it will have a machine capable of 360 teraflops by 2005, but Royyuru says advancing to a petaflop-speed machine will be "quite a jump," and he can't predict when a computer like that will be available.

Even after such a machine is delivered, it could still take decades to unravel the mysteries of protein folds, Royyuru says. But perhaps that effort will be aided by science that harkens back to techniques used to create elegant paper birds.

Copyright © 2004 IDG Communications, Inc.

It’s time to break the ChatGPT habit
Shop Tech Products at Amazon