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Cones, Curves, Shells, Towers: He Made Paper Jump to Life
By MARGARET WERTHEIM
 orrection Appended
SANTA
CRUZ, Calif. - On the mantel of a quiet suburban home here stands a curious
object resembling a small set of organ pipes nestled into a neat, white case.
At first glance it does not seem possible that such a complex, curving form
could have been folded from a single sheet of paper, and yet it was.
The construction is one of an astonishing collection of paper objects folded
by Dr. David Huffman, a former professor of computer science at the University
of California, Santa Cruz, and a pioneer in computational origami, an emerging
field with an improbable name but surprisingly practical applications.
Dr. Huffman died in 1999, but on a recent afternoon his daughter Elise Huffman
showed a visitor a sampling of her father's enigmatic models. In contrast
to traditional origami, where all folds are straight, Dr. Huffman developed
structures based around curved folds, many calling to mind seedpods and seashells.
It is as if paper has been imbued with life. In another innovative
approach, Dr. Huffman explored structures composed of repeating three-dimensional
units - chains of cubes and rhomboids, and complex tesselations of triangular,
pentagonal and star-shaped blocks. From the outside, one model appears to
be just a rolled-up sheet of paper, but looking down the tube reveals a miniature
spiral staircase. All this has been achieved with no cuts or glue, the one
classic origami rule that Dr. Huffman seemed inclined to obey. Derived
from the Japanese ori, to fold, and gami, paper, origami has come a long
way from cute little birds and decorative boxes. Mathematicians and scientists
like Dr. Huffman have begun mapping the laws that underlie folding, converting
words and concepts into algebraic rules. Computational origami, also known
as technical folding, or origami sekkei, draws on fields that include computational
geometry, number theory, coding theory and linear algebra. This weekend,
paper folders from around the nation will gather at the Fashion Institute
of Technology in New York for the annual convention of Origami USA. At an
adjacent conference on origami and education, Dr. Robert Lang, a leading
computational origamist, will give a talk on mathematics and its application
to origami design, including such real-world problems as folding airbags
and space-based telescopes. Dr. Lang, a laser physicist in Alamo, Calif.,
who trained at the California Institute of Technology, gave up that career
18 months ago to become a full-time folder. "Some people are peculiarly susceptible
to the charms of origami," he said, "and somewhere along the way the ranks
of the infected were joined by mathematicians." Dr. Lang is the author of
a recent book on technical folding, "Origami Design Secrets: Mathematical
Methods for an Ancient Art." Most computational origamists are driven
by sheer curiosity and the aesthetic pleasure of these structures, but their
work is also finding application in fields like astronomy and protein folding,
and even automobile safety. These days when Dr. Lang is not inventing new
models using a specialized origami software package he has developed, he
acts as an origami consultant. He has helped a German manufacturer design
folding patterns for airbags and advised astronomers on how to fold up a
huge flat-screen lens for a telescope based in space. Dr. Lang has
been studying Dr. Huffman's models and research notes, and is amazed at what
he has found. Although Dr. Huffman is a legend in the tiny world of origami
sekkei, few people have seen his work. During his life he published only
one paper on the subject. Dr. Huffman worked on his foldings from the early
1970's, and over the years, said Dr. Lang, "he anticipated a great deal of
what other people have since rediscovered or are only now discovering. At
least half of what he did is unlike anything I've seen." One of Dr.
Huffman's main interests was to calculate precisely what structures could
be folded to avoid putting strain on the paper. Through his mathematics,
he was trying to understand "when you have multiple folds coming into a point,
what is the relationship of the angles so the paper won't stretch or tear,''
said Dr. Michael Tanner, a former computer science colleague of Dr. Huffman
who is now provost and vice chancellor for academic affairs at the University
of Illinois in Chicago. What fascinated him above all else, Dr. Tanner
said, "was how the mathematics could become manifest in the paper. You'd
think paper can't do that, but he'd say you just don't know paper well enough."
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