OSCON 2005: Know When to Fold 'Em

by Daniel H. Steinberg

Open source developers spend their days solving ideas that range from the creative to the mundane. There are different challenges at the beginning of a project and at the end. Do you "build one to throw it away" or are some projects too complex to justify starting them over from scratch? How do you communicate your ideas once you have solved a particular problem, and how do you find and benefit from the work of others?

It turns out that those producing origami wrestle with these same issues every day. During the Thursday morning keynotes at O'Reilly's Open Source Conference (OSCON) 2005, Robert J. Lang explored some of the connections between origami and open source in a talk titled "Computational Origami from Flapping Birds to Space Telescopes." Lang explained that not only has open source software contributed to origami as an artform, but the development of origami has also served as an apt metaphor for open source.

Not Your Father's Flapping Bird

For hundreds of years, origami has most commonly been a figure folded from one sheet of paper with no cuts. The images that might come to mind are the polygonal representations of animals that you have come to accept as standing for a frog or a crane. New folders still begin with these traditional designs and build on well-known bases such as the kite base, the frog base, and the bird base.

But much about origami changed as we entered the modern era of folding about fifty years ago. Akira Yoshizawa created new figures of artistic beauty. His new creations were certainly groundbreaking and pushed the art in new directions, but Lang explained that an even more important contribution was Yoshizawa's language for communicating designs. "He developed a written instructional language. A way of presenting origami information. This was the Hypertext Transfer Protocol of origami. It was created in 1950 and we've had 50 years to build on it."

If you haven't seen examples of more modern origami and what is possible with a single piece or paper, follow the links to Lang's website for a look at a more realistic-looking frog than you are familiar with. The OSCON audience was amazed by the scaled koi fish and the snake with about one thousand scales. Lang said that he wasn't likely to fold either of those again.

Computers and Origami

In addition to the changes that followed Yoshizawa's introduction of symbols for communicating design, Lang attributes much of the progress in the field to the discovery of origami by scientists. He referred to these as artists applying mathematical principles to origami composition. In the last 50 years, the number of published designs grew from 100 to 10,000. There is a searchable online database located at

Lang has long investigated how computers can aid in the design of origami figures. The TreeMaker application allows you to start with a stick figure of an animal, say, a deer. You take careful measurements, and from the resulting weighted tree graph, you construct a system of equations describing the figure. For the deer example, there were 200 equations. The solution of the equations results in a crease pattern. Imagine unfolding an origami figure. All of the lines on the square piece of paper make up what is called the crease pattern. The TreeMaker application performs the analysis that leads to this solution.

The role of the computer is not limited to just aiding in design. Lang showed an oval tesselation. Here is the crease pattern (PDF) for the figure. In this case, the crease pattern was scribed by a laser. It was as if the entire figure was folded by machine.

Practical Applications

In every mathematics classroom, shortly after a teacher has finished the lesson of the day, some student will raise their hand and ask, "But when are we ever going to use this in real life?" This question didn't occur to anyone in the OSCON audience, as most attendees assumed that origami is a recreation that is enjoyable despite its lack of applications. Lang surprised the audience by presenting examples of where origami has been used in "real life."

In the first, he looked at the case of a giant lens that is to orbit in space so that people on Earth can use it to amplify the sky and so satellites can use it to photograph the Earth. The problem is launching this 100m-wide lens on a rocket. Lang helped determine how best to fold the lens so that it can be compactly stored for launch. He included this image of his work with a smaller prototype.

A second example centered around a heart stent. Although the scale of the problems differ, the central issue remains the same. With the stent, how do you alter the shaper so that the device can move through the arteries to the target area? You can see from this picture how the stent was designed to collapse.

Whether origami is being applied to scientific challenges, presented in its classical form, or used to create challenging, authentic representations, we admire and respect the work being presented. As to its ties to open source, there is a rich history of publishing clever designs. Many of these designs are maintained in repositories where they can remain free, as in beer.

Daniel H. Steinberg is the editor for the new series of Mac Developer titles for the Pragmatic Programmers. He writes feature articles for Apple's ADC web site and is a regular contributor to Mac Devcenter. He has presented at Apple's Worldwide Developer Conference, MacWorld, MacHack and other Mac developer conferences.

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