Origami

Origami (折り紙 or 折紙 origami "paper folding") is the art of paper folding. The goal of this art is to create a given result using geometric folds and crease patterns. The word literally means "paper folding" in Japanese and refers to all types of paper folding, even those of non-Japanese origin.

Origami only uses a small number of different folds, but they can be combined in a variety of ways to make intricate designs. In general, these designs begin with a square sheet of paper, whose sides may be different colors, and proceed without cutting the paper. 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 (Kirigami 切り紙) or starting with a rectangular, circular, or other non-square sheets of paper. It's also possible to create folds from triangular paper.

History

The "invention" of paper folding probably followed soon after the invention of paper itself. The earliest known traditions of paper folding were of ritual origin. The earliest known Japanese origami is probably ceremonial paper folding, such as noshi (熨斗), which started in Muromachi era (1392-1573). In Korea, ancestral tablets made of paper, known as jibang (지방), were folded in a prescribed manner handed down the family line for use in ancestral worship ceremonies. The earliest known European origami is probably the baptismal certificate of 16th century, represented by a little bird (pajarita in Spanish or cocotte in French).

An origami design can be as simple as a party hat or paper airplane, or as complex as a model of the Eiffel Tower, a leaping gazelle or a stegosaurus that takes an hour and a half to fold. Sometimes the most complex origami models must be folded from foil instead of paper; this allows more layers before the paper becomes impractically thick. Modern origami has broken free from the traditional linear construction techniques of the past, and models are now frequently wet-folded or constructed from materials other than paper and foil. The Japanese do not see origami as an art form, but rather as an integrated part of their culture and tradition.

Joseph Albers, the father of modern color theory and minimalistic art, taught origami and paper folding in the 1920s and 30s. His methods, which involved sheets of round paper that were folded into spirals and curved shapes, have influenced modern origami artists like Kunihiko Kasahara. Friedrich Fröbel, founder of the kindergartens, recognized paper binding, weaving, folding, and cutting as teaching aids for child development during the early 1800s.

The work of Akira Yoshizawa of Japan, a prolific creator of origami designs and writer of books on origami, inspired a modern renaissance of the craft. His work was promoted through the studies of Gershon Legman as published in the seminal books of Robert Harbin Paper Magic and more so in Secrets of the Origami Masters which revealed the wide world of paperfolding in the mid 1960s. Modern origami has attracted a worldwide following, with ever more intricate designs and new techniques such as 'wet-folding,' the practice of dampening the paper somewhat during folding to allow the finished product to hold shape better, and variations such as modular origami also known as unit origami, where many origami units are assembled to form an often decorative whole.

Recent historians have uncovered the lost origami Tamatebako, a model from the folk tale of "Urashima-Taro and the Tamatebako". A three volume wood cut book, "Ranma-Zushiki", published in 1734, contained two pictures that were identified by Yasuo Koyanagi in 1993 as the Tamatebako model. Masao Okamura, an origami historian, was able to recreate the model. The model, contrary to common theory of traditional origami, involved cutting and gluing.

One of the most famous origami designs is the Japanese crane. The crane is auspicious in Japanese culture. Japan has launched a satellite named tsuru (crane). Legend says that anyone who folds one thousand paper cranes will have their heart's desire come true. The origami crane (折鶴 orizuru in Japanese) has become a symbol of peace because of this legend, and because of a young Japanese girl named Sadako Sasaki. Sadako was exposed to the radiation of the atomic bombing of Hiroshima as an infant, and it took its inevitable toll on her health. She was then, a hibakusha -- an atom bomb survivor. By the time she was twelve in 1955, she was dying of leukemia. Hearing the legend, she decided to fold 1,000 cranes so that she could live. However, it was not just for herself that she wished healing. It is said that what made the girl truly special in her effort was her additional wish to end all such suffering, to bring peace and healing to the victims of the world.

Sadako folded 644 cranes before she died. Her classmates continued folding cranes in honor of their friend. Sadako was buried with a wreath of 1,000 cranes. While her effort could not extend her life, it moved her friends to make a granite statue of Sadako in the Hiroshima Peace Park: a young girl standing with her hand outstretched, a paper crane flying from her fingertips. Every year the statue is adorned with thousands of wreaths of a thousand origami cranes. A group of one thousand paper cranes is called senbazuru in Japanese.

The tale of Sadako has been dramatized in many books and movies. In one version, Sadako wrote a haiku that translates into English as:

Taking Origami developments into the 21st Century, designer Jay Cousins created a simpler form of Origami in plastic - dubbed orikaso. Influenced by the purity and beauty of Origami, and Japanese design principles, Orikaso processes can be used to create functional and useful products.

Basic instructions

Most origami folds can be broken down into simpler steps. A list of techniques is accumulating in the origami tech tree.

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 gsm can be used for simple folds, such as the crane and waterbomb.

Heavier weight papers of 100 gsm or more can be wetfolded. This technique allows for a more rounded sculpting of the model, which becomes rigid and sturdy when dry.

Kami is sold in prepackaged squares of various sizes ranging from 2.5 cm to 25 cm or more. It is commonly coloured on one side and white on the other; however, duo coloured kami and patterned kami exist and can be used effectively for colour-changed models. The weight of kami is slightly less than that of 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 adhered to a sheet of thin paper. Related to this is tissue foil, which is made by gluing a thin piece of tissue to kitchen aluminium 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. Both types of foil materials are suitable for complex models.

Artisan papers such as unryu, lokta, hanji, gampi, kozo, saa 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.

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.

Folding a flat model from a crease pattern has been proven by Marshall Bern and Barry Hayes to be NP complete. [1]

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 origami sekkei, 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 serendipidity. 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 pioneered 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 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.

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. Rather, 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.