Japanese origami

Art of folding objects out of paper without cutting, pasting, or decorating. Its early history is unknown, but it seems to have developed from the older art of folding cloth. Origami has reached its greatest development in Japan, with hundreds of traditional folds and an extensive literature dealing with the art. There are two types of Japanese folds: figures used in ceremonial etiquette, and objects such as animals, flowers, furniture, and human figures. Some objects have amusing action features; best known is the bird that flaps its wings when its tail is pulled. Paper folding has also flourished in Spain, South America, and Germany.

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(from oru meaning "folding", and kami meaning "paper") is the ancient Japanese art of paper folding. The goal of this art is to create a representation of an object using geometric folds and crease patterns preferably without the use of gluing or cutting the paper,and using only one piece of paper.

Origami only uses a small number of different folds, but they can be combined in a variety of ways to make intricate designs. The most well known form is probably the Japanese paper crane. In general, these designs begin with a square sheet of paper whose sides may be different colors or prints. Contrary to most popular belief, traditional Japanese origami, which has been practiced since the Edo era (1603–1867), has often been less strict about these conventions, sometimes cutting the paper during the creation of the design.

History

There is much speculation as to the origin of origami. It is safe to say that most of its development occurred in Japan; however, there have also been less developed (but independent) paperfolding traditions in China, Korea, Germany, and Spain, among other places.

Origami had already become a significant aspect of Japanese ceremony by the Heian period of Japanese history. Samurai warriors would exchange gifts adorned with noshi, a sort of good luck token made of folded strips of paper. Origami butterflies were used during the celebration of Shinto weddings to represent the bride and groom.

In the 1960s the art of origami began to spread out, first with modular origami and then with various movements developing, including kirigami. Origami is now an international art.

Paper and other materials

Although almost any laminar material can be used for folding, the choice of material used greatly affects the folding and final look of the model.

Normal copy paper with weights of 70–90 g/m² (19-24lb) can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of 100 g/m² (approx. 25lb) or more can be wet-folded. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when it is dry.

Special origami paper, often also referred to as "kami" (Japanese for paper, among other things), is sold in prepackaged squares of various sizes ranging from 2.5 cm to 25 cm or more. It is commonly colored on one side and white on the other; however, dual coloured and patterned versions exist and can be used effectively for color-changed models. Origami paper weighs slightly less than copy paper, making it suitable for a wider range of models.

Foil-backed paper, just as its name implies, is a sheet of thin foil glued to a sheet of thin paper. Related to this is tissue foil, which is made by gluing a thin piece of tissue paper to kitchen aluminum foil. A second piece of tissue can be glued onto the reverse side to produce a tissue/foil/tissue sandwich. Foil-backed paper is available commercially, but not tissue foil; it must be handmade. Both types of foil materials are suitable for complex models. is the predominant origami paper used in Japan. Washi is generally tougher than ordinary paper made from wood pulp, and is used in many traditional arts. Washi is commonly made using fibers from the bark of the gampi tree, the mitsumata shrub (Edgeworthia papyrifera), or the paper mulberry but also can be made using bamboo, hemp, rice, and wheat.

Artisan papers such as unryu, lokta, hanji, gampi, kozo, saa, and abaca have long fibres and are often extremely strong. As these papers are floppy to start with, they are often backcoated or resized with methylcellulose or wheat paste before folding. Also, these papers are extremely thin and compressible, allowing for thin, narrowed limbs as in the case of insect models.

Paper money from various countries are also popular to create origami with, called "Moneygami". It is common to create the figure depicted on the note itself.

Only paper is necessary to fold origami; however, some enthusiasts prefer to use a folding bone to sharpen creases while folding. Other folders grow certain nails long to aid with creasing instead of a folding bone.

Action Origami

Origami doesn't just cover still-lifes, it also covers moving objects; Origami can move in clever ways. Action origami includes origami that flies, requires inflation to complete, or, when complete, uses the kinetic energy of your hands, applied at a certain region on the model, to move another flap or limb. Some argue that strictly speaking, only the latter is really "recognized" as action origami. Action origami, first appearing with the traditional Japanese flapping bird, is quite common. One example is Robert Lang's instrumentalists; when the figures' heads are pulled away from their bodies, their hands will move, resembling the playing of music.

Mathematics of origami

The practice and study of origami encapsulates several subjects of mathematical interest. For instance, the problem of flat-foldability (whether a crease pattern can be folded into a 2-dimensional model) has been a topic of considerable mathematical study.

There are four mathematical rules for origami crease patterns:

1. crease patterns are two colorable
2. at any vertex the number of valley and mountain folds always differ by two in either direction
3. at any vertex, the sum of all the odd angles add up to 180 degrees, as do the even.
4. a sheet can never penetrate a fold

Significantly, paper exhibits zero Gaussian curvature at all points on its surface, and only folds naturally along lines of zero curvature. But the curvature along the surface of a non-folded crease in the paper, as is easily done with wet paper or a fingernail, is no longer subject to this constraint.

The problem of rigid origami ("if we replaced the paper with sheet metal and had hinges in place of the crease lines, could we still fold the model?") has great practical importance. For example, the Miura map fold is a rigid fold that has been used to deploy large solar panel arrays for space satellites.

Technical origami

Technical origami, also known as , is a field of origami that has developed almost hand-in-hand with the field of mathematical origami. In the early days of origami, development of new designs was largely a mix of trial-and-error, luck and serendipity. With advances in origami mathematics however, the basic structure of a new origami model can be theoretically plotted out on paper before any actual folding even occurs. This method of origami design was developed by Robert Lang, Meguro Toshiyuki and others, and allows for the creation of extremely complex multi-limbed models such as many-legged centipedes, human figures with a full complement of fingers and toes, and the like.

The main starting point for such technical designs is the crease pattern (often abbreviated as 'CP'), which is essentially the layout of the creases required to form the final model. Although not intended as a substitute for diagrams, folding from crease patterns is starting to gain in popularity, partly because of the challenge of being able to 'crack' the pattern, and also partly because the crease pattern is often the only resource available to fold a given model, should the designer choose not to produce diagrams. Still, there are many cases in which designers wish to sequence the steps of their models but lack the means to design clear diagrams. Such origamists occasionally resort to the Sequenced Crease Pattern (abbreviated as SCP) which is a set of crease patterns showing the creases up to each respective fold. The SCP eliminates the need for diagramming programs or artistic ability while maintaining the step-by-step process for other folders to see. Another name for the Sequenced Crease Pattern is the Progressive Crease Pattern (PCP).

Paradoxically enough, when origami designers come up with a crease pattern for a new design, the majority of the smaller creases are relatively unimportant and added only towards the completion of the crease pattern. What is more important is the allocation of regions of the paper and how these are mapped to the structure of the object being designed. For a specific class of origami bases known as 'uniaxial bases', the pattern of allocations is referred to as the 'circle-packing'. Using optimization algorithms, a circle-packing figure can be computed for any uniaxial base of arbitrary complexity. Once this figure is computed, the creases which are then used to obtain the base structure can be added. This is not a unique mathematical process, hence it is possible for two designs to have the same circle-packing, and yet different crease pattern structures. Other methods of design exist as well...Boxpleating, polygon packing. See Robert Langs Origami Design secrets for more information.

Space flight

There may soon be an origami airplane launched from space. A prototype passed a durability test in a wind tunnel on March 2008, and Japan's space agency adopted it for feasibility studies.

Gallery

Authors of books about origami

• Akira Yoshizawa - reinvented modern origami. Created the modern repertoire of folding symbols
• Robert J. Lang - Author of many Origami books including the new benchmark Origami Design Secrets
• Peter Engel - influential origami artist and theorist
• Tomoko Fuse (布施 知子) - famous for boxes and unit origami
• Robert Harbin - popularised origami in Britain; also presented a series of short programmes entitled Origami, made by Thames Television for ITV
• Eric Joisel - French wet-folder renowned for his life-like masks
• Kunihiko Kasahara - devised a standardized method for creating many modular polyhedra
• Duy Nguyen- master artist that wrote a lot of origami books
• John Montroll - probably the most prolific Western artist and author of over 16 books on origami
• Nick Robinson - origami artist and author of over a dozen books on origami
• Toshikazu Kawasaki - Japanese mathematician famous for his Iso-area folding theory and his many geometric folds, including Kawasaki's "Rose"
• Makoto Yamaguchi
• Jeremy Shafer - California origamian entertainer who folds whimsical designs
• Satoshi Kamiya - One of the youngest geniuses of the origami field
• Nicolas Terry - French artist known for his unique, cartoonish style
• Issei Yoshino - famed for his multimodular Tyrannosaurus and Triceratops skeletons
• Marc Kirschenbaum - known for his instrumentalist designs
• Didier Boursin
• :Florence Temko - a pioneer in spreading origami in the United States, is the most prolific author on this subject. With 55 books to her credit on paperarts and folk crafts, she has been a strong influence on interesting beginners in the art of paperfolding.
• David Shall - American designer, whose diagrams are completely hand drawn. Perhaps best known for his model of the Statue of Liberty

Groups and Organizations

• OrigamiUSA
• British Origami Society
• Origami Mitra, India

References

Further reading

• Robert J. Lang. The Complete Book of Origami: Step-by-Step Instructions in Over 1000 Diagrams. Dover Publications, Mineola, NY. Copyright 1988 by Robert J. Lang. ISBN 0-486-25837-8 (pbk.)

Pages 1-30 are an excellent introduction to most of these skills. Each of these 13 models is designed to let you practice one skill several times. Unfortunately, the remaining 24 models leave out lots of pre-creases. Many models are folded from non-square paper.

• Robert J. Lang. Origami Design Secrets: Mathematical Methods for an Ancient Art. A K Peters, Natick, MA. Copyright 2003 by A K Peters. ISBN 1-56881-194-2 (pbk)

This book shows how crease patterns and folding techniques are related to the large-scale structure of a model. It also shows how closed-unsinking was derived, using Lang's TreeMaker software for prototyping arbitrarily complex origami designs. Includes his famous super-complex "Black Forest Cuckoo Clock."

• Robert J. Lang. Origami in Action: Paper Toys that Fly, Flap, Gobble and Inflate. St. Martin's Griifin, 1997. ISBN 0312156189
• Tomoko Fuse. Unit Origami: Multidimensional Transformations. Japan Publications, inc. Tokyo. Copyright 1990 by Tomoko Fuse. ISBN 0-87040-852-6

This is an excellent book about modular origami, and serves as a great introduction to geometric models and designs.

• Kunihiko Kasahara. Origami Omnibus: Paper Folding for Everybody. Japan Publications, inc. Tokyo. Copyright 1988 by Kunihiko Kasahara. ISBN 4-8170-9001-4

A good book for a more advanced origamian, this book presents many more complicated ideas and theories, although the author tends to go off on long tangents about random topics. Still lots of good models though...

• Kunihiko Kasahara and Toshie Takahama. Origami for the Connoisseur. Japan Publications, inc. Tokyo. Copyright 1987 by Kunihiko Kasahara and Toshie Takahama. ISBN 0-87040-670-1

Another good book; same comments as the previous author.

• Satoshi Kamiya. Works by Satoshi Kamiya, 1995-2003. Origami House, Tokyo. Copyright 2005 by Satoshi Kamiya. ISBN 0000041944

An extremely complex book for the elite origamian, most models take 100+ steps to complete. Includes his famous Divine Dragon Bahamut and Ancient Dragons. Instructions are in Japanese and English.

• Issei Yoshino. Issei Super Complex Origami. Origami House, Tokyo.

Contains many complex models, notably his Samurai Helmet, Horse, and multimodular Triceratops skeleton. Instructions are in Japanese.

• Jeremy Shafer. Origami to Astonish and Amuse. St. Martin's Press, New York, NY. Copyright 2001 by Jeremy Shafer. ISBN 0-312-25404-0

A clever cornucopia of whimsical models, such as his Nail Clippers, Surfer on a Wave, Invisible Duck, Running Car, Monolithic Rubblestone boulder plus 84 others.

• One Thousand Paper Cranes: The Story of Sadako and the Children's Peace Statue by Takayuki Ishii, ISBN 0-440-22843-3
• Sadako and the Thousand Paper Cranes by Eleanor Coerr, ISBN 0-698-11802-2
• Origami 1, Robert Harbin, 1969, ISBN 0-340-10902-5
• Origami 2, Robert Harbin, ISBN 0-340-15384-9
• Origami 3, Robert Harbin, 1972, ISBN 0-340-16655-X
• Origami 4, Robert Harbin, 1977, ISBN 0-340-21822-3 (rare)
• Extreme Origami, Kunihiko Kasahara, 2001, ISBN 0-8069-8853-3
• Ariomar Ferreira da Silva. Brincando com Origami Arquitetônico: 16 diagrams. Global Editora, São Paulo, Brazil. Copyright 1991 by Ariomar Ferreira da Silva and Leôncio de O. Carvalho. ISBN 85-260-0273-2
• Masterworks of Paper Folding by Michael LaFosse
• Papercopia: Origami Designs by David Shall, 2008 ISBN 978-0-9796487-0-0. Contains diagrams for 24 original models by the author including Claw Hammer, Daffodil, Candlestick.

See also

External links

• OrigamiTube A user friendly origami instructional and origami related video site.
• British Origami Society The U.K.'s central origami organization.
• OrigamiUSA The biggest origami organization in the U.S.
• Origami.com Large collection of diagrams, suitable for beginners.
• Animated Origami Animated diagrams for beginners.
• Oriland.com Virtual Origami exhibition, Oriversity for beginners and 80 diagrams in Origami Studio.
• Large collection of diagrams, animated diagrams included, perfect for any skill level.
• Make-Origami