Origami
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Showing posts with label Types. Show all posts
Showing posts with label Types. Show all posts
Kirigami
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Kirie (切り紙?) is a variation of origami that includes cutting of the paper (from Japanese "kiru" = to cut, "kami" = paper). It is also called "Kirie" (切り絵). From "Kiru"= to cut, "e"= picture.
Typically, kirigami starts with a folded base, which is then cut; cuts are then opened and flattened to make the finished kirigami. Kirigami are usually symmetrical, such as snowflakes, pentagrams, or orchid blossoms.
The term Mon-Kiri is the Japanese art of paper cutting.
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Tessellations Origami
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A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M. C. Escher. Tessellations are seen throughout art history, from ancient architecture to modern art.
In Latin, tessella is a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellations, often made of glazed clay.
Tessellations and color
When discussing a tiling that is displayed in colors, to avoid ambiguity one needs to specify whether the colors are part of the tiling or just part of its illustration. See also symmetry.
The four color theorem states that for every tessellation of a normal Euclidean plane, with a set of four available colors, each tile can be colored in one color such that no tiles of equal color meet at a curve of positive length. Note that the coloring guaranteed by the four-color theorem will not in general respect the symmetries of the tessellation. To produce a coloring which does, as many as seven colors may be needed, as in the picture at right.
Tessellations with quadrilaterals
Copies of an arbitrary quadrilateral can form a tessellation with 2-fold rotational centers at the midpoints of all sides, and translational symmetry whose basis vectors are the diagonal of the quadrilateral or, equivalently, one of these and the sum or difference of the two. For an asymmetric quadrilateral this tiling belongs to wallpaper group p2. As fundamental domain we have the quadrilateral. Equivalently, we can construct a parallelogram subtended by a minimal set of translation vectors, starting from a rotational center. We can divide this by one diagonal, and take one half (a triangle) as fundamental domain. Such a triangle has the same area as the quadrilateral and can be constructed from it by cutting and pasting.
Regular and semi-regular tessellations
A regular tessellation is a highly symmetric tessellation made up of congruent regular polygons. Only three regular tessellations exist: those made up of equilateral triangles, squares, or hexagons. A semiregular tessellation uses a variety of regular polygons; there are eight of these. The arrangement of polygons at every vertex point is identical. An edge-to-edge tessellation is even less regular: the only requirement is that adjacent tiles only share full sides, i.e. no tile shares a partial side with any other tile. Other types of tessellations exist, depending on types of figures and types of pattern. There are regular versus irregular, periodic versus aperiodic, symmetric versus asymmetric, and fractal tessellations, as well as other classifications.
Penrose tilings using two different polygons are the most famous example of tessellations that create aperiodic patterns. They belong to a general class of aperiodic tilings that can be constructed out of self-replicating sets of polygons by using recursion.
A monohedral tiling is a tessellation in which all tiles are congruent. Spiral monohedral tilings include the Voderberg tiling discovered by Hans Voderberg in 1936, whose unit tile is a nonconvex enneagon; and the Hirschhorn tiling discovered by Michael Hirschhorn in the 1970s, whose unit tile is an irregular pentagon.
Self-dual tessellations
Tilings and honeycombs can also be self-dual. All n-dimensional hypercubic honeycombs with Schlafli symbols {4,3n−2,4}, are self-dual.
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Pure and Pureland Origami
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Pure Origami
Essentially, 'pure' origami refers to folding that requires:
- Only a square sheet of paper be used
- No decoration be done post the completion of folding
- That no tape, glue, or scissors be used in the folding process.
Pureland Origami
Essentially, 'pure' origami refers to folding that requires:
- Only a square sheet of paper be used
- No decoration be done post the completion of folding
- That no tape, glue, or scissors be used in the folding process.
Pure Origami is a relatively new invention. Making paper creations with folding and cutting was common in the past. The 200 year old book Senbazuru Orikata shows models where cuts have been made. There's no apology or "opps" involved, it was okay to have cuts. Even today, some Japanese origami books will have models that have cuts.
So given the above criteria, not all origami models out there in the world today are considered 'pure' origami designs. Designs such as Neal Elias' 'The Last Waltz', Llopio's moment of truth', etc require rectangular pieces of paper whereas tessellations can also be made from pentagons and hexagons.
Pureland Origami
Another type of kind referred to is 'Pureland' origami. So, what kind of Origami is this? Pureland origami refers to those models, which conform to the restriction of using only mountain and valley folds (hence the reference to 'land' in the type of origami) in addition to pure origami rules. This would mean that since only 2 types of folds are required, the folding process cannot be complicated with sinks, folds and the like.
In the late 1970's, John Smith developed the concept of "Pureland" origami. The rules in Pureland origami are the same as those for pure origami with the added restriction that only mountain and valley folds are allowed. The "land" part of Pureland comes from the fact that mountain and valley are elements of land.
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Modular origami
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Modular origami, or unit origami, is a paperfolding technique which uses multiple sheets of paper to create a larger and more complex structure than would be possible using single-piece origami techniques. Each individual sheet of paper is folded into a module, or unit, and then modules are assembled into an integrated flat shape or three-dimensional structure by inserting flaps into pockets created by the folding process. These insertions create tension or friction that holds the model together.
Modular origami forms may be flat or three-dimensional. Flat forms are usually polygons (sometimes known as coasters), stars, rotors, and rings. Three-dimensional forms tend to be regular polyhedra or tessellations of simple polyhedra.
There are some modular origami that are approximations of fractals, such as Menger's sponge. Macro-modular origami is a form of modular origami in which finished assemblies are themselves used as the building blocks to create larger integrated structures.
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Action Origami
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'Action origami' is origami that can be animated. The original traditional action model is the flapping bird. Typically models where the final assembly involves some special action, for instance blowing up a waterbomb, are also classed as action origami., More rarely models like paper plane and spinners which have no moving parts are included. Some traditional action origami involved cuts but modern models typically are built with no cuts. Action origami are normally toys built to amuse but some are designed to inspire wonder.
Action toys
Action toys include birds or butterflies with flapping wings, beaks that peck, and frogs that hop, as well as popular traditional models like the fortune teller. Bangers are models that make a nose when flicked down hard. Some action origami is designed to accompany a story whilst it is built.
Complex models
Some models are far more complex than can be classed as toys. They are built to amaze and astonish. For instance Robert J. Lang's Bassist, Pianist, and Violinist is a set of action models where each one plays an instrument when pulled on appropriately. Jeremy Shafer has made a number of extraordinary action models including a Swiss army knife with tools that open out, a slithering snake skin, and flashers one of which he demonstrated on the Carol Duvall Show.
Mathematical models
Flashers are models that can be folded up small and rapidly expanded. They have a regular pattern, the miura fold is a similar idea that has been used in commercial applications. Versions on a regular pattern can for instance be used to make a human figure when folded up or a maze when opened.
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Origami Types
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Below is a list of origami types featured in this web site. Each style of origami will produce a different genre of origami models.
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. read more . . .
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. read more . . .
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. read more . . .
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. read more . . .
- 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". read more . . .
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