The Origami Geometer 1999

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Curved-crease origami sculptures can self-fold into intricate patterns.

they looked beautiful. We’re still pursuing Q & A Erik Demaine unsolved mathematical problems too. David Huffman, who invented the compression algorithms used for mobile phones, left many beautiful origami sculptures when he died in

The origami geometer 1999. He was getting to the point at which he E. DEMAINE/M. DEMAINE Computer scientist Erik Demaine uses origami to advance computational geometry and create could conceive a 3D form, then reverse engi- art. His paper sculptures, made with his father, artist Martin Demaine, are now on show at the neer the steps to fold it with curved creases. Japanese American National Museum in Los Angeles, California; from August, the exhibition We hope to have him as a posthumous co- will tour the United States. He explains the challenges of folding together mathematics and art. author on some papers.

How do you actually fold the paper? How did you come to making one straight cut, then unfolding it? For prototype models we use a robotically do most of your work Houdini made a five-pointed star in this way controlled laser to score the paper, but we with your father? in the 1920s. It took us years to prove that you prefer a simple compass-like device. The NICK HIGGINS When I was five, I can make any straight-edged shape; we have final folding we always do by hand. At the helped him to design designed swans, butterflies and the MIT logo. first show we contributed to, we made three wire puzzles for toy Another result was an algorithm for folding sculptures by folding two circular pieces of shops across Canada. any three-dimensional (3D) shape out of one paper together using alternating pleats in He educated me him- sheet of paper. concentric circles. Curved-crease sculptures self as we travelled go back to a late-1920s design by the Bauhaus around the United Folding Paper: What is ‘self-folding’ origami? school in Germany. The surprising thing is The Infinite States. When I went Possibilities of It is a form in which the force of the creases how they self-fold into ornate forms from to university at the Origami pulls the material naturally into shape, with- these simple creases. For the Folding Paper age of 12, he attended Japanese American out any manipulation. We’re trying to find an exhibition, spanning the range of origami all my classes, mostly National Museum, Los algorithm to make any 3D shape with this art, we gave ourselves a little more power by computer science Angeles, California. method. One application would be a space manually joining a few key points together. and mathematics. March–August 2012. station that assembled itself in space. We Eventually, we started have devised a grid-based crease pattern that How did you come to study balloon animals? working together on mathematics and art. would allow a microscopic sheet to self-fold That was a collaboration with my father and He is now an artist in residence at the Mas- into any shape, in theory, by making cubes Vi Hart, a composer whose own father is a sachusetts Institute of Technology (MIT) in that stack together like 3D pixels. We haven’t mathematical sculptor. We noticed that bal- Cambridge, where I am a computer scientist. yet achieved self-folding at the nanoscale. loon animals could be seen as outlining the edges of a flat-sided 3D solid, and we found an How did you discover origami? What kind of origami are you doing now? algorithm that tells you how many balloons I heard about Robert Lang, a great origami We have been working with curved creases, you need to build a given solid. One appli- designer and physicist. Computational ori- the properties of which cation, conceived after the fact, would be to gami was just starting, and my father and I are poorly under- NATURE.COM build a pavilion from a single tube. But our became pioneers. Our first project was the stood. We were try- For more on maths motivation was just to play with balloons. ■ fold-and-cut problem: how many shapes ing out some curved and origami: can be made by folding a sheet of paper, patterns, and saw that go.nature.com/hittdq INTERVIEW BY JASCHA HOFFMAN