Origami

Origami (折り紙) 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. 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 nonsquare shapes to start with.

History
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 paperfolding 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 paperfolding 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 paperfolding in the west originated with the Moors much earlier, 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 paperfolding 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 japan, origami is a sport. every year, an origami tournament called Yaru Sano Origami is held in Kyoto.

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.

Techniques
Many origami books begin with a description of basic origami techniques which are used to construct the models. These include simple diagrams of basic folds like valley and mountain folds, pleats, reverse folds, squash folds, and sinks. There are also standard named bases which are used in a wide variety of models, for instance the bird base is an intermediate stage in the construction of the flapping bird.

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 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.

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 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; it must be handmade. Both types of foil materials are suitable for complex models.

Washi (和紙) 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 fibres 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 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.

Tools
It is common to fold using a flat surface but some folders like doing it in the air with no tools especially when displaying the folding. Many folders believe no tool should be used when folding. However a couple of tools can help especially with the more complex models. For instance a bone folder allows sharp creases to be made in the paper easily, paper clips can act as extra pairs of fingers, and tweezers can be used to make small folds. When making complex models from origami crease patterns, it can help to use a ruler and ballpoint embosser to score the creases. Completed models can be sprayed so they keep their shape better, and of course a spray is needed when wet folding.

Action 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


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
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 moulded 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
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
This 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 2 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.

Kirigami
In Kirigami it is allowed to make cuts. In traditional Origami, there was no Kirigami. Kirigami was simply called Origami. Just in the recent century the term Kirigami developed in order to distinguish it from "pure Origami"

Mathematics and 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.

Technical origami
Technical origami, also known as origami sekkei (折り紙設計), 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.

As a circle encloses the minimum amount of area for a given perimeter, circle packing allows for maximum efficiency in terms of paper usage. However, other polygonal shapes can be used to solve the packing problem as well. The use of polygonal shapes other than circles is often motivated by the desire to find easily locatable creases (such as multiples of 22.5 degrees) and hence an easier folding sequence as well. One popular offshoot of the circle packing method is box-pleating, where squares are used instead of circles. As a result, the crease pattern that arises from this method contains only 45 and 90 degree angles, which makes for easier folding.