[excerpted from:] Cones, Curves, Shells, Towers:
He Made Paper Jump to Life
By Margaret Wertheim for the NY Times, June 22, 2004
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
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
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.
Dr. Robert Lang, a leading computational origamist and 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. 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."
One of Dr. Huffman's discoveries was the critical "pi condition." This
says that if you have a point, or vertex, surrounded by four creases
and you want the form to fold flat, then opposite angles around the
vertex must sum to 180 degrees - or using the measure that mathematicians
prefer, to pi radians. Others have rediscovered that condition, Dr.
Lang said, and it has now generalized for more than four creases. In
this case, whatever the number of creases, all alternate angles must
sum to pi. How and under what conditions things can fold flat is a major
concern in computational origami.
Dr. Huffman's folding was a private activity. Professionally he worked
in the field of coding and information theory. As a student at M.I.T.
in the 1950's, he discovered a minimal way of encoding information known
as Huffman Codes, which are now used to help compress MP3 music files
and JPEG images. Dr. Peter Newman of the Computer Science Laboratory
at the Stanford Research Institute said that in everything Dr. Huffman
did, he was obsessed with elegance and simplicity. "He had an ability
to visualize problems and to see things that nobody had seen before,"
Dr. Newman said.
Like Mr. Resch, Dr. Huffman seemed innately attracted to elegant forms.
Before he took up paper folding, he was interested in what are called
"minimal surfaces," the shapes that soap bubbles make. He carried this
theme into origami, experimenting with ways that pleated patterns of
straight folds can give rise to curving three-dimensional surfaces.
Dr. Erik Demaine of M.I.T.'s Laboratory for Computer Science, who is
now pursuing similar research, described Dr. Huffman's work in this
area as "awesome."
Finally, Dr. Huffman moved into studying models in which the folds themselves
were curved. "We know almost nothing about curved creases," said Dr.
Demaine, who is using computer software to simulate the behavior of
paper under the influence of curving folds. Much of Dr. Huffman's research
was based on curves derived from conic sections, such as the hyperbola
and the ellipse.
His marriage of aesthetics and science has grown into a field that goes
well beyond paper. Dr. Tanner noted that his research is relevant to
real-world problems where you want to know how sheets of material will
behave under stress. Pressing sheet metal for car bodies is one example.
"Understanding what's going to happen to the metal,'' which will stretch,
"is related to the question of how far it is from the case of paper,"
which will not, Dr. Tanner said.
The mathematician G. H. Hardy wrote that "there is no permanent place
in the world for ugly mathematics." Dr. Huffman, who gave concrete form
to beautiful mathematical relations, would no doubt have agreed. In
a talk he gave at U.C. Santa Cruz in 1979 to an audience of artists
and scientists, he noted that it was rare for the two groups to communicate
with one another. "I don't claim to be an artist. I'm not even sure
how to define art," he said. "But I find it natural that the elegant
mathematical theorems associated with paper surfaces should lead to
visual elegance as well."
posted by www.skypape.com
Use of photos by permission of Huffman family, copyright Huffman 2008.
Photographer: Tony Grant.