The Arts : Origami

Origami (from ori meaning "folding", and kami meaning "paper") is the traditional Japanese folk art of paper folding, which started in the 17th century AD and was popularized in the mid-1900s. It has since then evolved into a modern art form. The goal of this art is to transform a flat sheet of material into a finished sculpture through folding and sculpting techniques, and as such the use of cuts or glue are not considered to be origami. The number of basic origami folds is small, but they can be combined in a variety of ways to make intricate designs. The most well known origami model 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 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 or using non-square shapes to start with.

There is much speculation as to the origin of origami. While Japan seems to have had the most extensive tradition, there is evidence of independent paper folding traditions in China, Germany and Spain, among other places. However because paper decomposes rapidly, there is very little direct evidence of its age or origins, aside from references in published material. The earliest evidence of paper folding in Europe is a picture of a small paper boat in Tractatus de sphaera mundi from 1490. There is also evidence of a cut and folded paper box from 1440. It is probable that paper folding in the west originated with the Moors much earlier, but it is not known if it was independently discovered or knowledge of origami came along the silk route.

In Japan, the earliest unambiguous reference to a paper model is in a short poem by Ihara Saikaku in 1680 which describes paper butterflies in a dream. Origami butterflies were used during the celebration of Shinto weddings to represent the bride and groom, so paper folding had already become a significant aspect of Japanese ceremony by the Heian period (794–1185) of Japanese history, enough that the reference in this poem would be recognized. Samurai warriors would exchange gifts adorned with noshi, a sort of good luck token made of folded strips of paper. In the early 1900s, Akira Yoshizawa, Kosho Uchiyama, and others began creating and recording original origami works. Akira Yoshizawa, in particular, was responsible for a number of innovations, such as wet-folding and the Yoshizawa-Randlett diagramming system, and his work inspired a renaissance of the art form. During the 1980s a number of folders started systematically studying the mathematical properties of folded forms, which led to a steady increase in the complexity of origami models, which continued well into the 1990s, after which some designers started returning to simpler forms.

Technique

The only material needed for origami is paper.  It should be thin, able to hold a crease, and not tear easily when folded a number of times.  Some origami paper is colored on one side, with white on the other.  Paper should always be folded on a hard, flat surface, and the folds should be as straight and precise as possible, with all corners and edges meeting evenly.  The standard folds are categorized into the following:

•             Valley Fold – The paper is folded downward, or toward you.  When unfolding the paper, the crease should always be on the bottom, resembling a valley.

•             Mountain Fold – In this case, the paper is folded backwards, or away from you.  When the paper is unfolded, the crease will be on the top, causing the paper to look like a mountain.

•             Crease – This is the line that remains as a result of a fold.

•             Top – The corner or edge of the paper that is pointed away from your body is considered to be the top.

•             Bottom – This is the corner or edge of the paper that is pointed toward your body.

•             Front – This is the side of the paper that is facing you as you work.

•             Back – The side of the paper that is facing the table is considered to be the back. 

•             Right – The parts that are lying to the right of the middle of the line.

•             Outside – This is the back and the front of your work.

•             Inside – This is everything that is between the front and the back layers of paper.

•             Unfold – This is the process of opening up a previous fold.

•             Turning – This is when the paper is turned (while still flat on the table) so that the corners are aligned.

•             Turning the Model Over – The paper is turned over so that the front becomes the back.

•             Outside Reverse Fold – The front and back layers of paper are spread apart and wrapped around the outside of the model, causing the edges that were originally valley folds to become mountain folds.

•             Inside Reverse Fold – An edge that is a mountain fold is pushed down between the front and back layers of the paper.  By doing this, the edge has become a valley fold.

Origami Paper

Almost any laminar material can be used for folding; the only requirement is that it should hold a crease. Origami paper, often referred to as "kami" (Japanese for paper), 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 colored 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. Normal copy paper with weights of 70–90 g/m² (19-24 lb) can be used for simple folds, such as the crane and waterbomb. Heavier weight papers of 100 g/m² (approx. 25 lb) 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.

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.

Washi is the traditional 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 fibers and are often extremely strong. As these papers are floppy to start with, they are often back-coated 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 is also popular to create origami with; this is known variously as Dollar Origami, Orikane, and Money Origami.

Towels and toilet paper are often folded by hotel staff to indicate to guests that the bathroom has been recently cleaned.

Types of Origami

Origami not only covers still-life, there are also 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 a person's 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.

Modular origami consists of putting a number of identical pieces together to form a complete model. Normally the individual pieces are simple but the final assembly may be tricky. Many of the modular origami models are decorative balls like kusudama, the technique differs though in that kusudama allows the pieces to be put together using thread or glue. Chinese paper folding includes a style called 3D origami where large numbers of pieces are put together to make elaborate models. Sometimes paper money is used for the modules. This style originated from some Chinese refugees while they were detained in America and is also called Golden Venture folding from the ship they came on.

Wet-folding is an origami technique for producing models with gentle curves rather than geometric straight folds and flat surfaces. The paper is dampened so it can be molded easily; the final model keeps its shape when it dries. It can be used, for instance, to produce very natural looking animal models.

Pureland origami is origami with the restriction that only one fold may be done at a time. More complex folds like reverse folds are not allowed, and all folds have straightforward locations. It was developed by John Smith in the 1970s to help inexperienced folders or those with limited motor skills. Some designers also like the challenge of creating good models within the very strict constraints.

Origami tessellations is a branch of origami is one that has grown in popularity recently, but has an extensive history. Tessellations refer to the tiling of the plane where a collection of two-dimensional figures fill a plane with no gaps or overlaps. Origami tessellations are tessellations made from a flat material, most often paper, but it can be from anything that holds a crease. The history of costuming includes tessellations done in fabric that are recorded as far back as the Egyptian Tombs. Fujimoto was an early Japanese Origami master who published books that included Origami tessellations, and in the 1960s there was a great exploration of tessellations by Ron Resch. Chris Palmer is an artist who has extensively explored tessellations and has found ways to create detailed Origami tessellations out of silk. Robert Lang and Alex Bateman are two designers who use computer programs to design Origami tessellations. The first American book on Origami tessellations was just published by Eric Gjerde, and the field has been expanding rapidly. There are numerous Origami tessellation artists including Chris Palmer (U.S.), Eric Gjerde (U.S.), Polly Verity (Scotland), Joel Cooper (U.S.), Christine Edison (U.S.), Ray Schamp (U.S.), Roberto Gretter (Italy), Goran Konjevod (U.S.),and Christiane Bettens (Switzerland) that are showing works that are both geometric and representational.

Practical Applications

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. 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. 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.

Thousand Origami Cranes

Thousand Origami Cranes (Senbazuru) is a group of one thousand origami paper cranes held together by strings. An ancient Japanese legend promises that anyone who folds a thousand origami cranes will be granted a wish by a crane, such as long life or recovery from illness or injury. The crane in Japan is one of the mystical or holy creatures (others include the dragon and the tortoise), and is said to live for a thousand years. In Asia, it is commonly said that folding 1000 paper origami cranes makes a person's wish come true. This makes them popular gifts for special friends and family.

A thousand paper cranes is also traditionally given as a wedding gift by the folder, who is wishing a thousand years of happiness and prosperity upon the couple. It can also be gifted to a new baby for long life and good luck. Hanging a Senbazuru in one's home is thought to be a powerfully lucky and benevolent charm. It is also used as a matchmaking charm for a Japanese girl when she turns 13 years old. She would make 1000 paper cranes and give it to an admired boy.

Sets of origami paper are sold widely in Japan, with Senbazuru sets including 1000 (or more, in case of mistakes) sheets of paper, string, and beads to place at the end of each string to prevent the cranes slipping off. Commonly the cranes are assembled as 25 strings of 40 cranes each. The size of the origami paper does not matter when assembling a thousand paper cranes, but smaller sheets consequently yield smaller and lighter strings of cranes. The most popular size for Senbazuru cranes is 75 by 75 millimeters (3.0 × 3.0 in). Some people cut their own squares of paper from anything available, such as magazines.

Origami paper used for Senbazuru is usually of a solid color, though printed designs are also available. Larger size origami paper, usually 6x6 inches, often has traditional Japanese or flower designs, reminiscent of kimono patterns.

The Thousand Origami Cranes has become a symbol of world peace through the story of Sadako Sasaki, a Japanese girl who tried to stave off her death from leukemia as a result of radiation from the atomic bombing of Hiroshima during World War II by making one thousand origami cranes, having folded only 644 before her death, and that her friends completed and buried them all with her. (This is only one version of the story. Hiroshima Peace Memorial Museum states that she did, in fact, complete the 1,000 cranes.) Her story is told in the book Sadako and the Thousand Paper Cranes. Several temples, including some in Tokyo and Hiroshima, have eternal flames for World Peace. At these temples, school groups or individuals often donate Senbazuru to add to the prayer for peace. The cranes are left exposed to the elements, slowly dissolving and becoming tattered as the wish is released. In this way they are related to the prayer flags of India and Tibet. In Western countries, the custom has been extended from giving a Senbazuru to cancer patients, to using them at funerals or on the grave.