Susan Orlean has been AWOL from the pages of the New Yorker for some time now, but she's back this week with a piece on origami and Robert Lang, former physicist and an acknowledged master of the craft.
He would have liked to have folded insects, but, in those years, bugs, as well as crustaceans, were still an origami impossibility. This was because no one had yet solved the problem of how to fold paper into figures with fat bodies and skinny appendages, so that most origami figures, even television characters and heads of state, still had the same basic shape as the paper cranes of nineteenth-century Japan. Then a few people around the globe had the idea that paper folding, besides being a pleasant diversion, might also have properties that could be analyzed and codified. Some started to study paper folding mathematically; others, including Lang, began devising mathematical tools to help with designing, all of which enabled the development of increasingly complex folding techniques. In 1970, no one could figure out how to make a credible-looking origami spider, but soon folders could make not just spiders but spiders of any species, with any length of leg, and cicadas with wings, and sawyer beetles with horns. For centuries, origami patterns had at most thirty steps; now they could have hundreds. And as origami became more complex it also became more practical. Scientists began applying these folding techniques to anything -- medical, electrical, optical, or nanotechnical devices, and even to strands of DNA -- that had a fixed size and shape but needed to be packed tightly and in an orderly way.
Lang's creations are truly astounding, almost to the point of being magical, because the comparison of the finished product to a flat, uncut sheet of paper is so dissonant. Here are two views of one of Lang's signature "bugs", a 7" silverfish he folded in 2004. The folding pattern is followed by the completed product:
In 1987, Lang folded a 15" long cuckoo clock out of a single sheet of paper. The clock, which "made Lang a sensation in the origami world", took him three months to design and six hours to fold. These days, he uses a computer program he wrote called TreeMaker to design his creations and a laser cutter borrowed from Squid Labs to gently score the paper for quicker & easier folding.
Squid Labs is responsible for a site called Instructables, which allows people to share step-by-step instructions for how to do just about anything, from broiled peanut butter and jelly sandwiches to origami. Lang doesn't seem to have any instructions for his designs up on Instructables, but he shares the site's open source and collaborative spirit...crease patterns for many of his most complex creations are available on his site and TreeMaker and ReferenceFinder are free to download (with the source code released under the GPL).
(Speaking of Instructables, here's an easy way to get started with origami. Just grab that stack of Post-It Notes sitting on your desk (the square ones, not the letterbox ones), peel the top one off, and follow these simple instructions to make a little box out of it. It'll take you 5 minutes...here's mine that I did this morning.)
For more on Robert Lang and origami, check out his web site (don't miss the foldable space telescope he's helping to build at the Lawrence Livermore National Laboratory), an audio recording of Lang's presentation from O'Reilly Media Open Source Conference 2005, an audio interview on The Connection, an interview with Cabinet magazine in 2005, and a more technical article by Lang on the mathematics and geometry of origami.
(As an aside, Lang's physics background and current vocation reminded me of Richard Feynman and his interest in flexagons, which are basically geometric origami shapes that can flexed into different shapes. A colleague of Feynman's invented the flexagon, which led to the formation of the Princeton Flexagon Committee, of which Feynman was a founding member.)
http://www.josephwu.com
Photo here; and Flúor, the design studio that created the exhibition.
When I was in high school we had a mathematician from Princeton come speak to my AP Comp Sci class, and he discussed how he was working on mathematically figuring out the best ways to pack 15-dimential spheres and such. It seemed like amazingly interesting work, but hopelessly without practical applications.
While reading about the origami this morning I though to myself that this was a much more real-world way to introduce people to that area of mathematics. I wish I had the math skills to work on this kind of stuff.
On a more serious note, there's some quality folded paper in the flickr origami groups.
I actually really like the crease patterns themselves. The one above looks like an intriguing piece of art, something that becomes something else...it's impossible to guess what it may become, which is part of the intrigue :-)
http://www.richardsweeney.co.uk/
For these complex designs, I wonder how large the beginning piece of paper is? It must be larger that the roughly 5" x 5" pieces that are part of beginner origami.
My 4-1/2 year old son and I are currently into creating paper snowflakes from cutting out pieces of folded triangles. His sense of wonder every time he opens a snowfake is priceless. I wonder about the mathmatics of paper snowflake creation...
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