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Tuesday, December 21, 2010

The Art of the Fold

"Spring into Action" by physicist and origami artist Jeff Beynon.
Origami is the art of paper folding (from the Japanese ori meaning "folding" and kami meaning "paper").  The term refers to all types of paper folding, even those not of Japanese origin.  In Japan origami is a folk art that goes back to the 17th century CE, and perhaps even earlier, but which became really popular in the mid-1900s.  However, there are paper folding traditions in China and Europe, notably Spain and Germany.  But since paper is so perishable, the only way of tracing its history is through references in published texts.

Image courtesy of Fabulous Papers.

In the early 1900s, origami artists began creating and recording original pieces.  Akira Yoshizawa created innovations such as wet-folding and a diagramming system, which created a renaissance for origami.  In the 1980s, a system-wide study of the mathematical properties of origami were explored, which led to a complexity of pieces which has gone on for decades.

Image courtesy of Fabulous Papers.

The number of folds can be small, but combined in a variety of ways they can make intricate designs.  Most designs begin with a square sheet of paper whose sides may be different colors or prints.  Traditional Japanese origami doesn't have strict rules, and sometimes cuts are made.  Modular origami, or unit folding, is a form that uses several sheets of paper for one design.  Each sheet of paper is folded into a module or unit, then assembled by inserting flaps into pockets, both accounted for in the design.  The tension created by the flaps and pockets holds the design together.

Kusudama (literally "medicine ball") is a form created by sewing multiple pyramidal units together through their points to create a spherical shape.  Sometimes a tassel is added, and they were once used for potpourri.  This can be similar to modular origami, but uses thread, glue, or tape to hold the piece together.


Sometimes paper money is used, also known jokingly as "moneygami".  This is thought to have originated with Chinese refugees detained in America.  It is also known by the name Golden Venture folding, named after the ship they came over on.

Origami presents several subjects of mathematical interest.  Technical origami, also known as origami sekkei, has developed on a parallel with mathematical origami.  In this field the basic structure of a design can be plotted out on paper or a computer before its execution.  This allows for the creation of extremely complex designs.

Image courtesy of Fabulous Papers.

The main starting point for these pre-conceived designs is the crease pattern, or CP, which is the layout of creases necessary for the final model.  This is different than a diagram, but is increasingly used instead of a diagram.  There is a challenge in "cracking" the pattern.  Some designers don't publish a diagram, so one is left with only the CP to complete the design.

Image courtesy of Fabulous Papers.

Some designers want to sequence the steps of their models but are unable to design clear diagrams, either due to lack of diagramming programs or artistic ability.  They occasionally use a Sequenced Crease Pattern (SCP) or Progressive Crease Patterns (PCP), which are names for a set of crease patterns.  This allows them to offer a step-by-step explanation.

Yoda courtesy of Fabulous Papers.

One of the foremost origami artists in the world is American physicist Dr. Robert J. Lang.  He is known for his intricate designs.  He has been involved in the mathematics of origami and in the use of computers to apply the theories of origami for real-world engineering applications.  Nine years ago he left the engineering field to become a full-time origami artist and consultant.  Yet he keeps his involvement in physics current with part-time laser consulting and as an editor of the Journal of Quantum Electronics.

Lang's Black Forest Cuckoo Clock

I, myself, have trouble remembering how to make an origami crane, so my hat's off to these brainiacs who can do so much more.

All images courtesy of Wikipedia unless otherwise noted.

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