An Origami Moment: Mathematics Meets Paper Folding in Los Angeles

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Origami has always been a cosmological art. The folder begins with a blank piece of paper - an empty, uniform space - then literally creates something out of nothing. Divinity looms in this act. Los Angeles is currently home to a rare constellation of origami projects; one could say that we are experiencing an origami moment.

'Mother and Child' by Christine Edison | Photo: International Arts & Artists.

At the Japanese American National Museum in Little Tokyo a spectacular exhibition showcases the potential enabled by the importation of scientific and mathematical techniques into this ancient art. Entitled Folding Paper: The Infinite Possibilities of Origami, the exhibit features works by leading practitioners of the new "technical folding", or origami sekkei, including physicist Robert Lang, mathematician Erik Demaine and software engineer Jeannine Mosely.

At the University of California Santa Cruz, visitors to the Eloise Pickard Smith gallery recently had the opportunity to see never-before exhibited works by mathematical origami pioneer David Huffman. And here in Los Angeles at the USC Libraries, Dr. Mosely and I are spearheading a project to build a giant fractal out of 49,000 business cards. Called the Mosely Snowflake Sponge, this trans-dimensional form pushes the limits of 'modular' origami both theoretically and practically; its construction is an experiment at the boundary of mathematics, art and engineering.

Mosely Snowflake Fractal at the USC Libraries | Photo: Nathan Masters.
Mosely Snowflake Fractal at the USC Libraries | Photo: Nathan Masters.
Mosely Snowflake Fractal at the USC Libraries | Photo: Paula Goldman.
Mosely Snowflake Fractal at the USC Libraries | Photo: Paula Goldman.

Like many people who are interested in technical folding, I learned about the subject through Dr. Robert Lang, an advisor to the show, co-editor of the book, Folding Paper: The Infinite Possibilities of Origami, and a laser physicist who gave up a career in optic fiber development to devote himself fulltime to origami. The move seemed insane from a professional perspective, but Lang was gripped by a fever that would not be denied and from the confines of his studio in a leafy suburb of Silicon Valley he has helped to foment a revolution. Over the past three decades he has developed a suite of computer programs that folders can use to create ever-more elaborate models of animals, reptiles and insects. Lang's enormous influence is felt throughout the JANM exhibition, which incorporates a bevy of miniature beasties, including one of his own signature mooses (he loves deers of all denominations and carefully folds the nuances of each species); a grasshopper by Brian Chan (who learned technical folding while studying mechanical engineering at MIT); and a stomping Styracosaurus by Japanese master Satoshi Kamiya - ire positively radiates from its tiny folded forelegs. My favourite pieces from this genre are French folder Eric Joisel's pangolin, a relative of the armadillo, represented here in breathtaking detail with hundreds of individual scales folded from a single sheet of paper, and Victoria Serova's magnificent "Double-Headed Eagle, Russian State Emblem". What one is struck by with all of these models is the scientist's attention to the specificity of anatomical features.

Eric Joisel | Photo: Japanese American National Museum.

The trend towards hyper-realism in this representational style of origami has its precedence in an earlier, scientifically inflected moment in the history of art - the Dutch realist painting of the seventeenth century. Here too artists strived to outdo one another in fidelity of detail. Usually the animals were dead in these paintings, shot or trapped by a hunter; or often the subjects were botanical - flowers and fruits were a favorite.

Jan Weenix, 1631. From the Akademie der Bildenden Künste, Gemäldegalerie (1631)

Running in parallel with the realist theme at the JANM exhibition is, from an art-historical viewpoint, its antithesis, a style of origami that falls in with the abstractions of modernism. In between the cases of creatures are works that riff on repetition, replication and recursion. Here we cross over from a classical conception of what 'art' might be (with all that implied about the value of the individual piece) into an arena heavily influenced by the aesthetics of "mechanical reproduction." This if the kind of origami that Huffman pioneered and it is here that the influence of mathematics is most evidently on show.


Huffman himself was an early leader in information theory and is famous for the invention of Huffman codes, now used in cell-phone communication. An extremely private man, few people were aware during his life of his paper-folding explorations (he passed away in 1999) and the recent exhibition at UCSC was the first time much of his oeuvre has been publically displayed. In 2004 I wrote about his achievements for the New York Times.

Huffman's aloofness was due in part due to a bitter dispute with another very private and prickly paper-folding genius named Ron Resch. In the 1960's and early 1970's both Huffman and Resch (a Buckminster Fuller-ish academic outsider and visionary) set out to explore what could be done with paper using mathematical rules. Neither had any interest in representation and both were entranced by geometric patterns. This strand of influence produces some of the most arresting works in the JANM exhibition, which includes one of Huffman's most technically difficult curved-crease pieces. But a curious lapse in the curatorial framing is the lack of acknowledgement for Resch. His "Paper and Stick Thing" film is a landmark work for anyone interested in this field and remains as astounding today as it must have been in 1969. You can see it now on You Tube.

Ron Resch

Traditional paper folding actually did include repetition in the form of 'modular origami', which entails construction from multiple repeated units. In the JANM show there are some exceptional works in this vein, including Jeannine Mosely's "Tricontahedral Orb", constructed out of curved components - a truly difficult act that extends Huffman's tradition and which the requires considerable mathematical analysis. Repetition also comes into play in origami tessellations, in which a single sheet of paper is pleated into complicated patterns. Standouts here include Christine Edison's "Snowstorm" and "Whirlpool Pattern" by Japanese modular master Tomoko Fuse.

Going through the JANM show one becomes aware of an unexpected gender dimension: There are almost no women doing representational origami - Serova remains the exception here - a fact that is acknowledged in the luscious catalog but which passes without further reflection. At the same time, women have produced many of the most interesting non-representational works; delicate, quiet, complicated pieces - often all in white - that without calling attention to themselves make you stop in wonderment. A parallel comes to mind here with the work of Eva Hesse and the drawings of Bridget Riley.

Nothing could be more repetitive than fractals, which, by definition, are a simple pattern recursively repeated. Fractals are geometrical forms that have non-integer dimensionality - instead of being clearly 2 or 3 dimensions, a fractal might have, say, 2.7 dimensions. The idea that one could fold fractals occurred to Mosely one morning in the early 1990's while she was playing with her infant son. At the time she was working as a software engineer designing 3-D modeling programs. Like Huffman she had trained at MIT and, like Resch, she had an uncanny ability to see spatial structures in her head. The company she worked for had just changed its address and she had a couple of thousand discarded business cards sitting in her basement. The idea came to her that she could fold them into a model of a fractal known as the Menger Sponge. Ten years and 66,000 business cards later the project was completed, and in 2006 I had the pleasure of curating an exhibition of this work at Machine Project. In the meantime Mosely had discovered a related fractal, which she named the Snowflake Sponge. When the USC Libraries invited me to curate a campus-wide project that would bring together students across the fields of the arts, sciences and engineering I jumped at the chance to bring this enigmatic object into being.

The Mosely Snowflake Sponge | Photo: Margaret Wertheim.
The Mosely Snowflake Sponge | Photo: Margaret Wertheim.

This time it will take 49,000 business cards, which have been specially designed to produce an Op-Art effect. Several thousand hours of human labor are being expended on the project and hundreds of students are folding component modules. In the process we are discovering unexpected symmetries and patterns within the form. Rather than re-presenting the anatomy of an existing animal, we are constructing an object that has hitherto only been imagined.


The Mosely Snowflake Sponge will be on display in the USC Doheny Library from September through December 2012. Construction workshops are taking place at the library during July and August.

Margaret Wertheim, the first Discovery Fellow at the USC Libraries, is director of the Institute For Figuring, a Los Angeles based organization devoted to the poetic and aesthetic dimensions of science and mathematics. The IFF's new exhibition space in Chinatown is open to the public Thursdays, Fridays and Saturdays 12 noon - 6:30pm.

For more information about the Mosely Snowflake Sponge project see the Institute For Figuring.


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