How to - Origami

Here is a presentation by Robert J. Lang at TED. It is titled Idea + Square = Origami.

The incredible revolution in origami design is expanding everywhere.

Here is the summary for this amazing presentation.

Origami dates back to 1797. For an art style that is so restrictive (folding only), it would seem that everything that can be done has been done. However, a Japanese origami artist called Yoshizawa, in the 20th century, created a common language used to describe origami models. The unique aspect of this language, is that it could describe selections and heredity, which could be then transformed into a computer language. At this point math was introduced to the art of origami.

Any origami model can be described as a crease pattern. A collection of folds on a single sheet of paper. A crease pattern follows four simple rules:

*2 color colorability (check Graph Theory)
*At any vertex, the difference between mountain folds and valley folds is always 2
*All odd and even angles add to a straight line
*No matter how you stack it, there are no overlapping folds, a sheet cannot penetrate a fold

These four rules can be easily handled by a computer.

Robert Lang’s Treemaker

The next step is to abstract an idea into a simple model that can be described to a computer. Robert Lang created a program called treemaker, where you input a stick figure or tree and it calculates the crease pattern required to generate a base with the amount of flaps described in it. Since a flap is nothing but a circular region of the paper, it becomes a problem of packing circles into a single sheet of paper. Lots of circles = lots of flaps.

This has lead to origami on demand, for commercial purposes and even for applications in real life problems. This new kind of origami has been applied in medicine, science, engineering and space. It basically solves the problem of turning a sheetlike object into a small bundle for transportation or storage purposes.

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