1.
Hindu temple architecture
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The Hindu temple architecture is an open, symmetry driven structure, with many variations, on a square grid of padas, depicting perfect geometric shapes such as circles and squares. In ancient Indian texts, a temple is a place for Tirtha - pilgrimage and it is a sacred site whose ambience and design attempts to symbolically condense the ideal tenets of Hindu way of life. The architectural principles of Hindu temples in India are described in Shilpa Shastras, susan Lewandowski states that the underlying principle in a Hindu temple is built around the belief that all things are one, everything is connected. A Hindu temple is meant to encourage reflection, facilitate purification of one’s mind, the specific process is left to the devotee’s school of belief. The primary deity of different Hindu temples varies to reflect this spiritual spectrum and these harmonious places were recommended in these texts with the explanation that such are the places where gods play, and thus the best site for Hindu temples. While major Hindu Mandirs are recommended at sangams, river banks, lakes and seashore, Brhat Samhita, here too, they recommend that a pond be built preferably in front or to the left of the temple with water gardens. If water is present naturally nor by design, water is symbolically present at the consecration of temple or the deity. A Hindu temple design follows a design called vastu-purusha-mandala. The name is a composite Sanskrit word with three of the most important components of the plan, mandala means circle, Purusha is universal essence at the core of Hindu tradition, while Vastu means the dwelling structure. The design lays out a Hindu temple in a symmetrical, self-repeating structure derived from central beliefs, myths, cardinality, the four cardinal directions help create the axis of a Hindu temple, around which is formed a perfect square in the space available. The circle of mandala circumscribes the square, the square is considered divine for its perfection and as a symbolic product of knowledge and human thought, while circle is considered earthly, human and observed in everyday life. The square is divided into perfect square grids, in large temples, this is often a 8x8 or 64 grid structure. In ceremonial temple superstructures, this is an 81 sub-square grid, the square is symbolic and has Vedic origins from fire altar, Agni. The alignment along cardinal direction, similarly is an extension of Vedic rituals of three fires and this symbolism is also found among Greek and other ancient civilizations, through the gnomon. The second design of 4 padas has a central core at the diagonal intersection. The 9 pada design has a sacred surrounded center, and is the template for the smallest temple, older Hindu temple vastumandalas may use the 9 through 49 pada series, but 64 is considered the most sacred geometric grid in Hindu temples. It is also called Manduka, Bhekapada or Ajira in various ancient Sanskrit texts, each pada is conceptually assigned to a symbolic element, sometimes in the form of a deity or to a spirit or apasara. The central square of the 64 is dedicated to the Brahman, in a Hindu temple’s structure of symmetry and concentric squares, each concentric layer has significance
2.
Islamic geometric patterns
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Islamic decoration, which tends to avoid using figurative images, makes frequent use of geometric patterns which have developed over the centuries. These may constitute the entire decoration, may form a framework for floral or calligraphic embellishments, interest in Islamic geometric patterns is increasing in the West, both among craftsmen and artists including M. C. Islamic art mostly avoids figurative images to avoid becoming objects of worship, Islamic geometric patterns derived from simpler designs used in earlier cultures, Greek, Roman, and Sasanian. They are one of three forms of Islamic decoration, the others being the based on curving and branching plant forms. Geometric designs and arabesques are forms of Islamic interlace patterns, david Wade states that Much of the art of Islam, whether in architecture, ceramics, textiles or books, is the art of decoration – which is to say, of transformation. Wade argues that the aim is to transfigure, turning mosques into lightness and pattern and she argues that beauty, whether in poetry or in the visual arts, was enjoyed for its own sake, without commitment to religious or moral criteria. Many Islamic designs are built on squares and circles, typically repeated, overlapped and interlaced to form intricate, a recurring motif is the 8-pointed star, often seen in Islamic tilework, it is made of two squares, one rotated 45 degrees with respect to the other. The fourth basic shape is the polygon, including pentagons and octagons, all of these can be combined and reworked to form complicated patterns with a variety of symmetries including reflections and rotations. Such patterns can be seen as mathematical tessellations, which can extend indefinitely and they are constructed on grids that require only ruler and compass to draw. Artist and educator Roman Verostko argues that such constructions are in effect algorithms, the circle symbolizes unity and diversity in nature, and many Islamic patterns are drawn starting with a circle. On this basis is constructed a star surrounded by six smaller irregular hexagons to form a tessellating star pattern. This forms the basic design which is outlined in white on the wall of the mosque and that design, however, is overlaid with an intersecting tracery in blue around tiles of other colours, forming an elaborate pattern that partially conceals the original and underlying design. A similar design forms the logo of the Mohammed Ali Research Center and he observed that many different combinations of polygons can be used as long as the residual spaces between the polygons are reasonably symmetrical. For example, a grid of octagons in contact has squares as the residual spaces, every octagon is the basis for an 8-point star, as seen at Akbars tomb, Sikandra. Hankin considered the skill of the Arabian artists in discovering suitable combinations of polygons and he further records that if a star occurs in a corner, exactly one quarter of it should be shown, if along an edge, exactly one half of it. The mathematical properties of the tile and stucco patterns of the Alhambra palace in Granada. Some authors have claimed on dubious grounds to have found most or all of the 17 wallpaper groups there, the earliest geometrical forms in Islamic art were occasional isolated geometric shapes such as 8-pointed stars and lozenges containing squares. These date from 836 in the Great Mosque of Kairouan, Tunisia, the next development, marking the middle stage of Islamic geometric pattern usage, was of 6- and 8-point stars, which appear in 879 at the Ibn Tulun Mosque, Cairo, and then became widespread
3.
Selimiye Mosque
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The Selimiye Mosque is an Ottoman imperial mosque, which is located in the city of Edirne, Turkey. The mosque was commissioned by Sultan Selim II, and was built by architect Mimar Sinan between 1569 and 1575 and it was considered by Sinan to be his masterpiece and is one of the highest achievements of Islamic architecture. This grand mosque stands at the center of a külliye which comprises a medrese, a dar-ül hadis, a timekeepers room, in this mosque Sinan employed an octagonal supporting system that is created through eight pillars incised in a square shell of walls. The four semi domes at the corners of the square behind the arches spring from the pillars, are intermediary sections between the huge encompassing dome and the walls. While conventional mosques were limited by an interior, Sinans effort at Edirne was a structure that made it possible to see the mihrab from any location within the mosque. Surrounded by four minarets, the Mosque of Selim II has a grand dome atop it. Around the rest of the mosque were many additions, libraries, schools, hospices, baths, soup kitchens for the poor, markets, hospitals, and these annexes were aligned axially and grouped, if possible. In front of the mosque sits a rectangular court with an equal to that of the mosque. The innovation however, comes not in the size of the building, the mihrab is pushed back into an apse-like alcove with a space with enough depth to allow for window illumination from three sides. This has the effect of making the panels of its lower walls sparkle with natural light. The amalgamation of the hall forms a fused octagon with the dome-covered square. Formed by eight massive dome supports, the octagon is pierced by four half dome covered corners of the square, the beauty resulting from the conformity of geometric shapes engulfed in each other was the culmination of Sinans lifelong search for a unified interior space. At the Bulgarian siege of Edirne in 1913, the dome of the mosque was hit by Bulgarian artillery, owing to the domes extremely sturdy construction, the mosque survived the assault with only minor damage. On Mustafa Kemal Pashas order, it has not been restored since then, some damage can be seen on the image of the dome above, at and near the dark red calligraph to the immediate left of the central blue area. The mosque was depicted on the reverse of the Turkish 10,000 lira banknotes of 1982-1995, the mosque, together with its külliye, was included on UNESCOs World Heritage List in 2011. Selimiye Mosque was built at the peak of Ottoman military and cultural power, as the empire started to grow, the emperor had found an immediate urge to centralize the city. Sinan was asked to help to construct the Selimiye Mosque, making the mosque distinctive, like all other Ottoman mosques in the earlier periods, the Selimiye Mosque had a multitude of little domes and half domes. However, the limit in building Selimiye was to viewing the mosque as a unit from inside or outside rather than separate masses
4.
Edirne
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Edirne served as the third capital city of the Ottoman Empire from 1363 to 1453, before Constantinople became the empires fourth and final capital. At present, Edirne is the capital of Edirne Province in Turkish Thrace, the citys estimated population in 2014 was 165,979. The city was founded as Hadrianopolis, named for the Roman Emperor Hadrian and this name is still used in the Modern Greek. The name Adrianople was used in English, until the Turkish adoption of Latin alphabet in 1928 made Edirne the internationally recognized name. The Turkish, Edirne, Bulgarian, Одрин, Albanian, Edrêne, Slovene, Одрин and Serbian, Једрене / Jedrene are adapted forms of the name Hadrianopolis or of its Turkish version, see also its other names. The area around Edirne has been the site of no fewer than 16 major battles or sieges, military historian John Keegan identifies it as the most contested spot on the globe and attributes this to its geographical location. According to Greek mythology, Orestes, son of king Agamemnon, built this city as Orestias, at the confluence of the Tonsus and the Ardiscus with the Hebrus. The city was founded eponymously by the Roman Emperor Hadrian on the site of a previous Thracian settlement known as Uskadama, Uskudama, Uskodama or Uscudama and it was the capital of the Bessi, or of the Odrysians. Hadrian developed it, adorned it with monuments, changed its name to Hadrianopolis after himself, licinius was defeated there by Constantine I in 323, and Emperor Valens was killed by the Goths in 378 during the Battle of Adrianople. In 813, the city was seized by Khan Krum of Bulgaria who moved its inhabitants to the Bulgarian lands towards the north of the Danube. During the existence of the Latin Empire of Constantinople, the Crusaders were decisively defeated by the Bulgarian Emperor Kaloyan in the Battle of Adrianople. Later Theodore Komnenos, Despot of Epirus, took possession of it in 1227, in 1369, the city was conquered by the Ottoman sultan Murad I. The city remained the Ottoman capital for 90 years until 1453, Edirne is famed for its many mosques, domes, minarets, and palaces from the Ottoman period. Under Ottoman rule, Edirne was the city of the administrative unit, the eponymous Eyalet of Edirne, and after land reforms in 1867. Sultan Mehmed II, the conqueror of Constantinople, was born in Edirne, Sultan Mehmed IV left the palace in Constantinople and died in Edirne in 1693. During his exile in the Ottoman Empire, the Swedish king Charles XII stayed in the city during most of 1713, baháulláh, the founder of the Baháí Faith, lived in Edirne from 1863 to 1868. He was exiled there by the Ottoman Empire before being banished further to the Ottoman penal colony in Akka and he referred to Edirne in his writings as the Land of Mystery. Edirne was briefly occupied by imperial Russian troops in 1829 during the Greek War of Independence, the city suffered a fire in 1905
5.
Self-similarity
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In mathematics, a self-similar object is exactly or approximately similar to a part of itself. Many objects in the world, such as coastlines, are statistically self-similar. Self-similarity is a property of fractals. Scale invariance is a form of self-similarity where at any magnification there is a smaller piece of the object that is similar to the whole. For instance, a side of the Koch snowflake is both symmetrical and scale-invariant, it can be continually magnified 3x without changing shape, the non-trivial similarity evident in fractals is distinguished by their fine structure, or detail on arbitrarily small scales. As a counterexample, whereas any portion of a line may resemble the whole. It happens if the quantity f exhibits dynamic scaling, the idea is just an extension of the idea of similarity of two triangles. Note that two triangles are similar if the values of their sides are different however the corresponding dimensionless quantities, such as their angles. In mathematics, self-affinity is a feature of a fractal whose pieces are scaled by different amounts in the x- and this means that to appreciate the self similarity of these fractal objects, they have to be rescaled using an anisotropic affine transformation. We call L = a self-similar structure, the homeomorphisms may be iterated, resulting in an iterated function system. The composition of functions creates the algebraic structure of a monoid, when the set S has only two elements, the monoid is known as the dyadic monoid. The dyadic monoid can be visualized as a binary tree, more generally, if the set S has p elements. The automorphisms of the monoid is the modular group, the automorphisms can be pictured as hyperbolic rotations of the binary tree. A more general notion than self-similarity is Self-affinity, the Mandelbrot set is also self-similar around Misiurewicz points. Self-similarity has important consequences for the design of networks, as typical network traffic has self-similar properties. For example, in engineering, packet switched data traffic patterns seem to be statistically self-similar. This property means that simple models using a Poisson distribution are inaccurate, andrew Lo describes stock market log return self-similarity in econometrics. Finite subdivision rules are a technique for building self-similar sets, including the Cantor set
6.
Apophysis (software)
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Apophysis is an open source fractal flame editor and renderer for Microsoft Windows and Macintosh. Users can export fractalflames to other fractal flame rendering programs, such as FLAM3, there is a separate version of Apophysis that has support for 3D. There are numerous clones, ports, and forks of it, scott Draves invented Fractal Flames and published an open source implementation written in C in the early 90s. In 2001 Ronald Hordijk translated his code into Delphi and created a non-animated screensaver, and in 2003 or 2004 Mark Townsend took Ronalds code and added a graphical user interface to create Apophysis. It has since improved and updated by Peter Sdobnov, Piotr Borys. Since 2009, there is a version of Apophysis called Apophysis 7X, originally, it was targeting to provide support for modern Microsoft Windows operating systems like Windows Vista and 7. A strong feedback from the Apophysis users encouranged the developer Georg Kiehne to provide updates which made 7X the most popular and advanced version of Apophysis so far. Apophysis uses the Scripter Studio scripting library to allow users to write scripts which run and either create a new flame, edit the existing flames, one such instance is rendering an entire batch of fractals. Apophysis supports a plugin API so that new variations can be developed and distributed. There are numerous plugins available from the user communities. Fractal flame Fractal-generating software Fractal art Ultra Fractal Chaotica Official website Apophysis on SourceForge. net
7.
Multibrot set
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The name is a portmanteau of multiple and Mandelbrot set. Z ↦ z d + c. where d ≥2, the exponent d may be further generalized to negative and fractional values. The case of d =2 is the classic Mandelbrot set from which the name is derived, the sets for other values of d also show fractal images when they are plotted on the complex plane. Each of the examples of various powers d shown below is plotted to the same scale, values of c belonging to the set are black. The example d =2 is the original Mandelbrot set, the examples for d >2 are often called Multibrot sets. These sets include the origin and have fractal perimeters, with rotational symmetry. When d is negative the set surrounds but does not include the origin, there is interesting complex behaviour in the contours between the set and the origin, in a star-shaped area with -fold rotational symmetry. An alternative method is to render the exponent along the vertical axis and this requires either fixing the real or the imaginary value, and rendering the remaining value along the horizontal axis. The resulting set rises vertically from the origin in a column to infinity. The first prominent bump or spike is seen at an exponent of 2, the third image here renders on a plane that is fixed at a 45-degree angle between the real and imaginary axes. All the above images are rendered using an Escape Time algorithm that identifies points outside the set in a simple way, much greater fractal detail is revealed by plotting the Lyapunov exponent, as shown by the example below. The Lyapunov exponent is the error growth-rate of a given sequence, first calculate the iteration sequence with N iterations, then calculate the exponent as λ =1 N ln | z | and if the exponent is negative the sequence is stable. The white pixels in the picture are the parameters c for which the exponent is positive aka unstable, the colours show the periods of the cycles which the orbits are attracted to. All points colored dark-blue are attracted by a point, all points in the middle are attracted by a period 2 cycle. ESCAPE TIME ALGORITHM For each pixel on the screen do, The complex value z has coordinates on the plane and is raised to various powers inside the iteration loop by codes shown in this table. Powers not shown in the table can be obtained by concatenating the codes shown
8.
Algorithmic art
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Algorithmic art, also known as algorithm art, is art, mostly visual art, of which the design is generated by an algorithm. Algorithmic artists are sometimes called algorists, algorithmic art, also known as computer-generated art, is a subset of generative art and is related to systems art. Fractal art is an example of algorithmic art, the final output is typically displayed on a computer monitor, printed with a raster-type printer, or drawn using a plotter. Variability can be introduced by using pseudo-random numbers, there is no consensus as to whether the product of an algorithm that operates on an existing image can still be considered computer-generated art, as opposed to computer-assisted art. Some of the earliest known examples of computer-generated algorithmic art were created by Georg Nees, Frieder Nake, A. Michael Noll, Manfred Mohr and these artworks were executed by a plotter controlled by a computer, and were therefore computer-generated art but not digital art. The act of creation lay in writing the program, which specified the sequence of actions to be performed by the plotter and her early work with copier and telematic art focused on the differences between the human hand and the algorithm. Aside from the work of Roman Verostko and his fellow algorists. These are important here because they use a different means of execution, whereas the earliest algorithmic art was drawn by a plotter, fractal art simply creates an image in computer memory, it is therefore digital art. The native form of an artwork is an image stored on a computer –this is also true of very nearly all equation art. However, in a stricter sense fractal art is not considered algorithmic art, from one point of view, for a work of art to be considered algorithmic art, its creation must include a process based on an algorithm devised by the artist. This input may be mathematical, computational, or generative in nature, inasmuch as algorithms tend to be deterministic, meaning that their repeated execution would always result in the production of identical artworks, some external factor is usually introduced. This can either be a number generator of some sort. By this definition, fractals made by a program are not art. However, defined differently, algorithmic art can be seen to include fractal art, the artist Kerry Mitchell stated in his 1999 Fractal Art Manifesto, Fractal Art is not. Computer Art, in the sense that the computer does all the work. The work is executed on a computer, but only at the direction of the artist, turn a computer on and leave it alone for an hour. When you come back, no art will have been generated, algorist is a term used for digital artists who create algorithmic art. Algorists formally began correspondence and establishing their identity as artists following a panel titled Art, the co-founders were Roman Verostko and Jean-Pierre Hébert. Fractal art consists of varieties of computer-generated fractals with colouring chosen to give an attractive effect, especially in the western world, it is not drawn or painted by hand
9.
Fractal
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A fractal is a mathematical set that exhibits a repeating pattern displayed at every scale. It is also known as expanding symmetry or evolving symmetry, if the replication is exactly the same at every scale, it is called a self-similar pattern. An example of this is the Menger Sponge, Fractals can also be nearly the same at different levels. This latter pattern is illustrated in small magnifications of the Mandelbrot set, Fractals also include the idea of a detailed pattern that repeats itself. Fractals are different from other geometric figures because of the way in which they scale, doubling the edge lengths of a polygon multiplies its area by four, which is two raised to the power of two. Likewise, if the radius of a sphere is doubled, its volume scales by eight, but if a fractals one-dimensional lengths are all doubled, the spatial content of the fractal scales by a power that is not necessarily an integer. This power is called the dimension of the fractal. As mathematical equations, fractals are usually nowhere differentiable, the term fractal was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning broken or fractured, there is some disagreement amongst authorities about how the concept of a fractal should be formally defined. Mandelbrot himself summarized it as beautiful, damn hard, increasingly useful, Fractals are not limited to geometric patterns, but can also describe processes in time. Fractal patterns with various degrees of self-similarity have been rendered or studied in images, structures and sounds and found in nature, technology, art, Fractals are of particular relevance in the field of chaos theory, since the graphs of most chaotic processes are fractal. The word fractal often has different connotations for laypeople than for mathematicians, the mathematical concept is difficult to define formally even for mathematicians, but key features can be understood with little mathematical background. If this is done on fractals, however, no new detail appears, nothing changes, self-similarity itself is not necessarily counter-intuitive. The difference for fractals is that the pattern reproduced must be detailed, a regular line, for instance, is conventionally understood to be 1-dimensional, if such a curve is divided into pieces each 1/3 the length of the original, there are always 3 equal pieces. In contrast, consider the Koch snowflake and it is also 1-dimensional for the same reason as the ordinary line, but it has, in addition, a fractal dimension greater than 1 because of how its detail can be measured. This also leads to understanding a third feature, that fractals as mathematical equations are nowhere differentiable, in a concrete sense, this means fractals cannot be measured in traditional ways. The history of fractals traces a path from chiefly theoretical studies to modern applications in computer graphics, according to Pickover, the mathematics behind fractals began to take shape in the 17th century when the mathematician and philosopher Gottfried Leibniz pondered recursive self-similarity. In his writings, Leibniz used the term fractional exponents, also in the last part of that century, Felix Klein and Henri Poincaré introduced a category of fractal that has come to be called self-inverse fractals
10.
Computer art
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Computer art is any art in which computers play a role in production or display of the artwork. Such art can be an image, sound, animation, video, CD-ROM, DVD-ROM, video game, website, algorithm, performance or gallery installation. Many traditional disciplines are now integrating digital technologies and, as a result, for instance, an artist may combine traditional painting with algorithm art and other digital techniques. As a result, defining computer art by its end product can thus be difficult, Computer art is by its nature evolutionary since changes in technology and software directly affect what is possible. Notable artists in this vein include Manfred Mohr, Ronald Davis, Harold Cohen, Joseph Nechvatal, George Grie, Olga Kisseleva, John Lansdown, and Jean-Pierre Hébert. On the title page of the magazine Computers and Automation, January 1963, Edmund Berkeley published a picture by Efraim Arazi from 1962 and this picture inspired him to initiate the first Computer Art Contest in 1963. The annual contest was a key point in the development of art up to the year 1973. The precursor of computer art dates back to 1956-1958, with the generation of what is probably the first image of a human being on a computer screen, a pin-up girl at a SAGE air defense installation. Desmond Paul Henry invented the Henry Drawing Machine in 1960, his work was shown at the Reid Gallery in London in 1962, many artists tentatively began to explore the emerging computing technology for use as a creative tool. In the summer of 1962, A. Michael Noll programmed a computer at Bell Telephone Laboratories in Murray Hill. His later computer-generated patterns simulated paintings by Piet Mondrian and Bridget Riley, Noll also used the patterns to investigate aesthetic preferences in the mid-1960s. The Stuttgart exhibit featured work by Georg Nees, the New York exhibit featured works by Bela Julesz, a third exhibition was put up in November 1965 at Galerie Wendelin Niedlich in Stuttgart, Germany, showing works by Frieder Nake and Georg Nees. Analogue computer art by Maughan Mason along with computer art by Noll were exhibited at the AFIPS Fall Joint Computer Conference in Las Vegas toward the end of 1965. In 1968, the Institute of Contemporary Arts in London hosted one of the most influential exhibitions of computer art called Cybernetic Serendipity. The exhibition included many of whom often regarded as the first digital artists, Nam June Paik, Frieder Nake, Leslie Mezei, Georg Nees, A. Michael Noll, John Whitney, one year later, the Computer Arts Society was founded, also in London. At the time of the opening of Cybernetic Serendipity, in August 1968 and it took up the European artists movement of New Tendencies that had led to three exhibitions in Zagreb of concrete, kinetic, and constructive art as well as op art and conceptual art. New Tendencies changed its name to Tendencies and continued with more symposia, exhibitions, a competition, katherine Nash and Richard Williams published Computer Program for Artists, ART1 in 1970. Xerox Corporation’s Palo Alto Research Center designed the first Graphical User Interface in the 1970s, the first Macintosh computer is released in 1984, since then the GUI became popular
11.
Digital art
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Digital art is an artistic work or practice that uses digital technology as an essential part of the creative or presentation process. Since the 1970s, various names have been used to describe the process including computer art and multimedia art, more generally the term digital artist is used to describe an artist who makes use of digital technologies in the production of art. In an expanded sense, digital art is a term applied to art that uses the methods of mass production or digital media. The techniques of art are used extensively by the mainstream media in advertisements. Desktop publishing has had a impact on the publishing world. Both digital and traditional artists use many sources of electronic information, digital art can be purely computer-generated or taken from other sources, such as a scanned photograph or an image drawn using vector graphics software using a mouse or graphics tablet. Andy Warhol created digital art using a Commodore Amiga where the computer was introduced at the Lincoln Center. An image of Debbie Harry was captured in monochrome from a video camera, Warhol manipulated the image adding colour by using flood fills. The simplest is 2D computer graphics which reflect how you might draw using a pencil, in this case, however, the image is on the computer screen and the instrument you draw with might be a tablet stylus or a mouse. What is generated on screen might appear to be drawn with a pencil. The second kind is 3D computer graphics, where the screen becomes a window into a virtual environment, where you arrange objects to be photographed by the computer. A possible third paradigm is to art in 2D or 3D entirely through the execution of algorithms coded into computer programs. That is, it cannot be produced without the computer, fractal art, Datamoshing, algorithmic art and real-time generative art are examples. There are many programs for doing this. Pop surrealist artist Ray Caesar works in Maya, using it to create his figures as well as the realms in which they exist. Computer-generated animations are created with a computer, from digital models created by the 3D artists or procedurally generated. The term is applied to works created entirely with a computer. Movies make heavy use of computer-generated graphics, they are called computer-generated imagery in the film industry, a number of modern films have been noted for their heavy use of photo realistic CGI
12.
New media art
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The term differentiates itself by its resulting cultural objects and social events, which can be seen in opposition to those deriving from old visual arts. New Media Art often involves interaction between artist and observer or between observers and the artwork, which responds to them, such insights emphasize the forms of cultural practice that arise concurrently with emerging technological platforms, and question the focus on technological media, per se. The origins of new media art can be traced to the moving photographic inventions of the late 19th century such as the zoetrope, in 1958 Wolf Vostell becomes the first artist who incorporates a television set into one of his works. This installation is part of the collection of the Berlinische Galerie, a. Michael Noll, and multimedia performances of E. A. T. In 1983, Roy Ascott introduced the concept of distributed authorship in his worldwide telematic project La Plissure du Texte for Frank Poppers Electra at the Musée dArt Moderne de la Ville de Paris. Simultaneously advances in biotechnology have allowed artists like Eduardo Kac to begin exploring DNA. Influences on new media art have been the theories developed around interaction, hypertext, databases, important thinkers in this regard have been Vannevar Bush and Theodor Nelson, whereas comparable ideas can be found in the literary works of Jorge Luis Borges, Italo Calvino, and Julio Cortázar. These elements have been especially revolutionary for the field of narrative and anti-narrative studies, leading explorations into areas such as non-linear and this should be taken into account in examining the several themes addressed by new media art. This is a key concept since people acquired the notion that they were conditioned to view everything in a linear, now, art is stepping out of that form and allowing for people to build their own experiences with the piece. Non-linearity describes a project that escape from the linear narrative coming from novels, theater plays. Non-linear art usually requires audience participation or at least, the fact that the visitor is taken into consideration by the representation, altering the displayed content. The participatory aspect of new art, which for some artists has become integral, emerged from Allan Kaprows Happenings and became with Internet. Art is not produced as a completed object submitted to the audience appreciation, many new media art projects also work with themes like politics and social consciousness, allowing for social activism through the interactive nature of the media. One of the key themes in new art is to create visual views of databases. Pioneers in this area include Lisa Strausfeld, Martin Wattenberg and Alberto Frigo, the emergence of 3D printing has introduced a new bridge to new media art, joining the virtual and the physical worlds. The rise of technology has allowed artists to blend the computational base of new media art with the traditional physical form of sculpture. A pioneer in this field was artist Jonty Hurwitz who created the first known anamorphosis sculpture using this technique, currently, research projects into New media art preservation are underway to improve the preservation and documentation of the fragile media arts heritage. In New Media programs, students are able to get acquainted with the newest forms of creation and communication, New Media students learn to identify what is or isnt new about certain technologies
13.
Mathematical beauty
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Mathematical beauty describes the notion that some mathematicians may derive aesthetic pleasure from their work, and from mathematics in general. They express this pleasure by describing mathematics as beautiful, Mathematicians describe mathematics as an art form or, at a minimum, as a creative activity. Comparisons are often made music and poetry. The true spirit of delight, the exaltation, the sense of being more than Man, Paul Erdős expressed his views on the ineffability of mathematics when he said, Why are numbers beautiful. Its like asking why is Beethovens Ninth Symphony beautiful, if you dont see why, someone cant tell you. If they arent beautiful, nothing is, Mathematicians describe an especially pleasing method of proof as elegant. Depending on context, this may mean, A proof that uses a minimum of additional assumptions or previous results, a proof that is unusually succinct. A proof that derives a result in a surprising way A proof that is based on new, a method of proof that can be easily generalized to solve a family of similar problems. In the search for an elegant proof, mathematicians often look for different independent ways to prove a result—the first proof that is found may not be the best. The theorem for which the greatest number of different proofs have been discovered is possibly the Pythagorean theorem, another theorem that has been proved in many different ways is the theorem of quadratic reciprocity—Carl Friedrich Gauss alone published eight different proofs of this theorem. Some mathematicians see beauty in mathematical results that establish connections between two areas of mathematics that at first sight appear to be unrelated and these results are often described as deep. While it is difficult to find agreement on whether a result is deep. One is Eulers identity, e i π +1 =0 and this is a special case of Eulers formula, which the physicist Richard Feynman called our jewel and the most remarkable formula in mathematics. Other examples of deep results include unexpected insights into mathematical structures, for example, Gausss Theorema Egregium is a deep theorem which relates a local phenomenon to a global phenomenon in a surprising way. In particular, the area of a triangle on a surface is proportional to the excess of the triangle. Another example is the theorem of calculus. The opposite of deep is trivial, sometimes, however, a statement of a theorem can be original enough to be considered deep, even though its proof is fairly obvious. In his A Mathematicians Apology, Hardy suggests that a proof or result possesses inevitability, unexpectedness
14.
Generative art
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Generative art refers to art that in whole or in part has been created with the use of an autonomous system. An autonomous system in context is generally one that is non-human and can independently determine features of an artwork that would otherwise require decisions made directly by the artist. In some cases the human creator may claim that the system represents their own artistic idea. Generative art is used to refer to algorithmic art. But generative art can also be made using systems of chemistry, biology, mechanics and robotics, smart materials, manual randomization, mathematics, data mapping, symmetry, tiling, the use of the word generative in the discussion of art has developed over time. The use of Artificial DNA defines an approach to art focused on the construction of a system able to generate unpredictable events. The use of systems, required by some contemporary definitions. This approach is also named emergent, while Nees does not himself remember, this was the title of his doctoral thesis published a few years later. The correct title of the first exhibition and catalog was computer-grafik, Generative art and related terms was in common use by several other early computer artists around this time, including Manfred Mohr. The term Generative Art with the meaning of dynamic artwork-systems able to generate multiple artwork-events was clearly used the first time for the Generative Art conference in Milan in 1998. The term has also used to describe geometric abstract art where simple elements are repeated, transformed. Thus defined, generative art was practised by the Argentinian artists Eduardo McEntyre, in 1972 the Romanian-born Paul Neagu created the Generative Art Group in Britain. It was populated exclusively by Neagu using aliases such as Hunsy Belmood, in 1972 Neagu gave a lecture titled Generative Art Forms at the Queens University, Belfast Festival. In 1970 the School of the Art Institute of Chicago created a department called Generative Systems, in 1989 Franke referred to generative mathematics as the study of mathematical operations suitable for generating artistic images. From the mid-1990s Brian Eno popularized the terms generative music and generative systems, making a connection with earlier music by Terry Riley, Steve Reich. From the end of the 20th century, communities of artists, designers, musicians and theoreticians began to meet. The first meeting about generative Art was in 1998, at the inaugural International Generative Art conference at Politecnico di Milano University, in Australia, the Iterate conference on generative systems in the electronic arts followed in 1999. On-line discussion has centred around the eu-gene mailing list, which began late 1999 and these activities have more recently been joined by the Generator. x conference in Berlin starting in 2005
15.
Abstract art
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Abstract art uses a visual language of shape, form, color and line to create a composition which may exist with a degree of independence from visual references in the world. Western art had been, from the Renaissance up to the middle of the 19th century, underpinned by the logic of perspective, the arts of cultures other than the European had become accessible and showed alternative ways of describing visual experience to the artist. By the end of the 19th century many artists felt a need to create a new kind of art which would encompass the fundamental changes taking place in technology, science and philosophy. The sources from which individual artists drew their theoretical arguments were diverse, Abstract art, non-figurative art, non-objective art, and nonrepresentational art are loosely related terms. They are similar, but perhaps not of identical meaning, Abstraction indicates a departure from reality in depiction of imagery in art. This departure from accurate representation can be slight, partial, or complete, even art that aims for verisimilitude of the highest degree can be said to be abstract, at least theoretically, since perfect representation is likely to be exceedingly elusive. Artwork which takes liberties, altering for instance color and form in ways that are conspicuous, total abstraction bears no trace of any reference to anything recognizable. In geometric abstraction, for instance, one is unlikely to find references to naturalistic entities, Figurative art and total abstraction are almost mutually exclusive. But figurative and representational art often contains partial abstraction, both geometric abstraction and lyrical abstraction are often totally abstract. It is at level of visual meaning that abstract art communicates. One can enjoy the beauty of Chinese calligraphy or Islamic calligraphy without being able to read it, in Chinese painting, abstraction can be traced to the Tang dynasty painter Wang Mo, who is credited to have invented the splashed-ink painting style. While none of his paintings remain, this style is seen in some Song Dynasty Paintings. A late Song painter named Yu Jian, adept to Tiantai buddhism and his paintings show heavily misty mountains in which the shapes of the objects are barely visible and extremely simplified. This type of painting was continued by Sesshu Toyo in his later years, another instance of abstraction in Chinese painting is seen in Zhu Deruns Cosmic Circle. The painting is a reflection of the Daoist metaphysics in which chaos, in Tokugawa Japan some zen monk-painters created Enso, a circle who represents the absolute enlightenment. Usually made in one spontaneous brush stroke, it became the paradigm of the minimalist aesthetic that guided part of the zen painting, three art movements which contributed to the development of abstract art were Romanticism, Impressionism and Expressionism. Artistic independence for artists was advanced during the 19th century, patronage from the church diminished and private patronage from the public became more capable of providing a livelihood for artists. Expressionist painters explored the use of paint surface, drawing distortions and exaggerations
16.
Fractal-generating software
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Fractal-generating software is any computer program that generates images of fractals. There are many fractal generating programs available, both free and commercial, many different features are included in fractal-generating software packages. Some fractal software packages allow for the creation of movies from a sequence of fractal images, some standard graphics software contains filters or plug-ins which can be used for fractal generation. Many stand-alone fractal-generating programs can be used in conjunction with other programs to create more complex images. There are many fractal generating programs available, both free and commercial, fractal art Fractal-generating software at DMOZ
17.
Julia set
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In the context of complex dynamics, a topic of mathematics, the Julia set and the Fatou set are two complementary sets defined from a function. Thus the behavior of the function on the Fatou set is regular, the Julia set of a function f is commonly denoted J, and the Fatou set is denoted F. These sets are named after the French mathematicians Gaston Julia and Pierre Fatou whose work began the study of complex dynamics during the early 20th century. Let f be a rational function from the plane into itself, that is, f = p / q. Then there is a number of open sets F1. Fr, that are invariant by f and are such that. In the first case the cycle is attracting, in the second it is neutral and these sets Fi are the Fatou domains of f, and their union is the Fatou set F of f. The complement of F is the Julia set J of f, J is a nowhere dense set and an uncountable set. Like F, J is left invariant by f, and on set the iteration is repelling, meaning that | f − f | > | z − w | for all w in a neighbourhood of z. This means that f behaves chaotically on the Julia set, although there are points in the Julia set whose sequence of iterations is finite, there are only a countable number of such points. The sequences generated by points outside this set behave chaotically, a phenomenon called deterministic chaos, there has been extensive research on the Fatou set and Julia set of iterated rational functions, known as rational maps. For example, it is known that the Fatou set of a map has either 0,1,2 or infinitely many components. Each component of the Fatou set of a map can be classified into one of four different classes. J is the smallest closed set containing at least three points which is invariant under f. J is the closure of the set of repelling periodic points, for all but at most two points z ∈ X, the Julia set is the set of limit points of the full backwards orbit ⋃ n f − n. If f is a function, then J is the boundary of the set of points which converge to infinity under iteration. If f is a polynomial, then J is the boundary of the filled Julia set, that is, there are two Fatou domains, the interior and the exterior of the circle, with iteration towards 0 and ∞, respectively. For g = z 2 −2 the Julia set is the segment between −2 and 2
18.
Mandelbrot set
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Its definition and name are due to Adrien Douady, in tribute to the mathematician Benoit Mandelbrot. The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes, Mandelbrot set images may be created by sampling the complex numbers and determining, for each sample point c, whether the result of iterating the above function goes to infinity. If c is constant and the initial value of z 0 is variable instead. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications, the style of this repeating detail depends on the region of the set being examined. The sets boundary also incorporates smaller versions of the shape, so the fractal property of self-similarity applies to the entire set. The Mandelbrot set has become popular outside mathematics both for its appeal and as an example of a complex structure arising from the application of simple rules. It is one of the examples of mathematical visualization. The Mandelbrot set has its place in complex dynamics, a field first investigated by the French mathematicians Pierre Fatou and this fractal was first defined and drawn in 1978 by Robert W. Brooks and Peter Matelski as part of a study of Kleinian groups. On 1 March 1980, at IBMs Thomas J. Watson Research Center in Yorktown Heights, New York, Mandelbrot studied the parameter space of quadratic polynomials in an article that appeared in 1980. The mathematicians Heinz-Otto Peitgen and Peter Richter became well known for promoting the set with photographs, books, the cover article of the August 1985 Scientific American introduced a wide audience to the algorithm for computing the Mandelbrot set. The cover featured an image created by Peitgen, et al, the Mandelbrot set became prominent in the mid-1980s as a computer graphics demo, when personal computers became powerful enough to plot and display the set in high resolution. The Mandelbrot set is the set of values of c in the plane for which the orbit of 0 under iteration of the quadratic map z n +1 = z n 2 + c remains bounded. That is, a number c is part of the Mandelbrot set if, when starting with z0 =0 and applying the iteration repeatedly. This can also be represented as z n +1 = z n 2 + c, c ∈ M ⟺ lim sup n → ∞ | z n +1 | ≤2. For example, letting c =1 gives the sequence 0,1,2,5,26, as this sequence is unbounded,1 is not an element of the Mandelbrot set. On the other hand, c = −1 gives the sequence 0, −1,0, which is bounded, and so −1 belongs to the Mandelbrot set. The Mandelbrot set M is defined by a family of quadratic polynomials P c, C → C given by P c, z ↦ z 2 + c. For each c, one considers the behavior of the sequence obtained by iterating P c starting at critical point z =0, the Mandelbrot set is defined as the set of all points c such that the above sequence does not escape to infinity
19.
Icon
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An icon is a religious work of art, most commonly a painting, from Eastern Christianity and certain Eastern Catholic churches. The most common subjects include Christ, Mary, saints and/or angels, icons may also be cast in metal, carved in stone, embroidered on cloth, painted on wood, done in mosaic or fresco work, printed on paper or metal, etc. Comparable images from Western Christianity are generally not described as icons, Eastern Orthodox tradition holds that the creation of Christian images dates back to the very early days of Christianity, and there is has been a continuous tradition since then. The icons of later centuries can be linked, often closely, to images from the 5th century onwards, there was enormous destruction of images during the Byzantine Iconoclasm of 726-842, although this did settle for good the question of the appropriateness of images. Since then icons have had a continuity of style and subject. At the same time there has been change and development, Christian tradition dating from the 8th century identifies Luke the Evangelist as the first icon painter. Aside from the legend that Pilate had made an image of Christ and he relates that King Abgar of Edessa sent a letter to Jesus at Jerusalem, asking Jesus to come and heal him of an illness. In this version there is no image, further legends relate that the cloth remained in Edessa until the 10th century, when it was taken to Constantinople. It went missing in 1204 when Crusaders sacked Constantinople, but by then numerous copies had firmly established its iconic type. They crown these images, and set them up along with the images of the philosophers of the world that is to say, with the images of Pythagoras, and Plato, and Aristotle, and the rest. They have also other modes of honouring these images, after the manner of the Gentiles. And he called him and said, Lycomedes, what do you mean by this matter of the portrait, can it be one of thy gods that is painted here. For I see that you are living in heathen fashion. Later in the passage John says, But this that you have now done is childish and imperfect, at least some of the hierarchy of the Christian churches still strictly opposed icons in the early 4th century. At the Spanish non-ecumenical Synod of Elvira bishops concluded, Pictures are not to be placed in churches, so that they do not become objects of worship and adoration. to our religion. After the emperor Constantine I extended official toleration of Christianity within the Roman Empire in 313 and this period of Christianization probably saw the use of Christian images became very widespread among the faithful, though with great differences from pagan habits. Robin Lane Fox states By the early century, we know of the ownership of private icons of saints. 480-500, we can be sure that the inside of a saints shrine would be adorned with images and votive portraits, when Constantine himself apparently converted to Christianity, the majority of his subjects remained pagans
20.
Iteration
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Iteration is the act of repeating a process, either to generate an unbounded sequence of outcomes, or with the aim of approaching a desired goal, target or result. Each repetition of the process is called an iteration. In the context of mathematics or computer science, iteration is a building block of algorithms. Iteration in mathematics may refer to the process of iterating a function i. e. applying a function repeatedly, iteration of apparently simple functions can produce complex behaviours and difficult problems - for examples, see the Collatz conjecture and juggler sequences. Another use of iteration in mathematics is in iterative methods which are used to produce approximate solutions to certain mathematical problems. Newtons method is an example of an iterative method, manual calculation of a numbers square root is a common use and a well-known example. Iteration in computing is the marking out of a block of statements within a computer program for a defined number of repetitions. That block of statements is said to be iterated, a computer scientist might also refer to block of statements as an iteration. In the example above, the line of code is using the value of i as it increments and this idea is found in the old adage, Practice makes perfect. Unlike computing and math, educational iterations are not predetermined, instead, in algorithmic situations, recursion and iteration can be employed to the same effect. Some types of programming languages, known as functional programming languages, are designed such that they do not set up block of statements for explicit repetition as with the for loop, instead, those programming languages exclusively use recursion. Each piece of work will be divided repeatedly until the amount of work is as small as it can possibly be, the algorithm then reverses and reassembles the pieces into a complete whole. The classic example of recursion is in list-sorting algorithms such as Merge Sort, the code below is an example of a recursive algorithm in the Scheme programming language that will output the same result as the pseudocode under the previous heading. In Object-Oriented Programming, an iterator is an object that ensures iteration is executed in the way for a range of different data structures, saving time. An iteratee is an abstraction which accepts or rejects data during an iteration, recursion Fractal Iterated function Infinite compositions of analytic functions
21.
Fibonacci word
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A Fibonacci word is a specific sequence of binary digits. The Fibonacci word is formed by repeated concatenation in the way that the Fibonacci numbers are formed by repeated addition. It is an example of a Sturmian word. The name “Fibonacci word” has also used to refer to the members of a formal language L consisting of strings of zeros. Any prefix of the specific Fibonacci word belongs to L, L has a Fibonacci number of members of each possible length. Let S0 be 0 and S1 be 01, now S n = S n −1 S n −2. The infinite Fibonacci word is the limit S ∞, enumerating items from the above definition produces, S00 S101 S2010 S301001 S401001010 S50100101001001. The nth digit of the word is 2 + ⌊ n φ ⌋ − ⌊ φ ⌋ where φ is the golden ratio, alternatively, one can imagine directly generating the entire infinite Fibonacci word by the following process, start with a cursor pointing to the single digit 0. Then, at each step, if the cursor is pointing to a 0, append 1,0 to the end of the word, in either case, complete the step by moving the cursor one position to the right. The resulting sequence begins 0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0,1,0,1,1,0,1,1,0,1,0,1,1,0. However this sequence differs from the Fibonacci word only trivially, by swapping 0s for 1s and shifting the positions by one. A closed form expression for the so-called rabbit sequence, The nth digit of the word is ⌊ n φ ⌋ − ⌊ φ ⌋ −1 where φ is the golden ratio and ⌊ x ⌋ is the floor function. The word is related to the sequence of the same name in the sense that addition of integers in the inductive definition is replaced with string concatenation. This causes the length of Sn to be Fn +2, also the number of 1s in Sn is Fn and the number of 0s in Sn is Fn +1. The infinite Fibonacci word is not periodic and not ultimately periodic, the last two letters of a Fibonacci word are alternately 01 and 10. Suppressing the last two letters of a Fibonacci word, or prefixing the complement of the last two letters, creates a palindrome, example,01 S4 =0101001010 is a palindrome. The palindromic density of the infinite Fibonacci word is thus 1/φ, where φ is the Golden ratio, in the infinite Fibonacci word, the ratio / is φ, as is the ratio of zeroes to ones. The infinite Fibonacci word is a sequence, Take two factors of the same length anywhere in the Fibonacci word
22.
Mandelbulb
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The Mandelbulb is a three-dimensional fractal, constructed by Daniel White and Paul Nylander using spherical coordinates in 2009. A canonical 3-dimensional Mandelbrot set does not exist, since there is no 3-dimensional analogue of the 2-dimensional space of complex numbers and it is possible to construct Mandelbrot sets in 4 dimensions using quaternions. However, this set does not exhibit detail at all scales like the 2D Mandelbrot set does. The Mandelbulb is then defined as the set of c in ℝ3 for which the orbit of ⟨0,0,0 ⟩ under the iteration v ↦ v n + c is bounded. For n >3, the result is a 3-dimensional bulb-like structure with fractal surface detail, many of their graphic renderings use n =8. However, the equations can be simplified into rational polynomials when n is odd. For example, in the case n =3, the power can be simplified into the more elegant form. More general fractals can be found by setting v n, = r n ⟨ sin cos , sin sin , cos ⟩ for functions f and g. So this gives, for example, x → x 2 − y 2 − z 2 + x 0 y →2 x z + y 0 z →2 x y + z 0 or various other permutations. This quadratic formula can be applied several times to get many power-2 formulae, so this gives, x → x 3 −3 x + x 0 or other permutations. Y → − y 3 +3 y x 2 − y z 2 + y 0 z → z 3 −3 z x 2 + z y 2 + z 0 for example. This reduces to the complex fractal w → w 3 + w 0 when z=0, there are several ways to combine two such cubic transforms to get a power-9 transform which has slightly more structure. For example, take the case of z → z 5 + z 0, the case z → z 9 gives a Mandelbulb most similar to the first example where n=9. A more pleasing result for the power is got basing it on the formula. This fractal has cross-sections of the power 9 Mandelbrot fractal and it has 32 small bulbs sprouting from the main sphere. A perfect spherical formula can be defined as a formula, → where n = f 2 + g 2 + h 2 where f, g and h are nth power rational trinomials, the cubic fractal above is an example. In the Disney movie Big Hero 6, the climax takes place in the middle of a wormhole
23.
Koch snowflake
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The Koch snowflake is a mathematical curve and one of the earliest fractal curves to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled On a continuous curve without tangents, the progression for the area of the snowflake converges to 8/5 times the area of the original triangle, while the progression for the snowflakes perimeter diverges to infinity. Consequently, the snowflake has an area bounded by an infinitely long line. The Koch snowflake can be constructed by starting with a triangle, then recursively altering each line segment as follows. Draw an equilateral triangle that has the middle segment from step 1 as its base, remove the line segment that is the base of the triangle from step 2. After one iteration of this process, the shape is the outline of a hexagram. The Koch snowflake is the limit approached as the steps are followed over and over again. The Koch curve originally described by Helge von Koch is constructed with one of the three sides of the original triangle. In other words, three Koch curves make a Koch snowflake, the Koch curve has an infinite length because the total length of the curve increases by one third with each iteration. Each iteration creates four times as many segments as in the previous iteration. Hence the length of the curve after n iterations will be n times the original triangle perimeter, which is unbounded as n tends to infinity. As the number of iterations tends to infinity, the limit of the perimeter is, lim n → ∞ P n = lim n → ∞3 ⋅ s ⋅ n = ∞, a ln 4/ln 3-dimensional measure exists, but has not been calculated so far. Only upper and lower bounds have been invented, collapsing the geometric sum gives, A n = a 0 = a 05. The limit of the area is, lim n → ∞ A n = lim n → ∞ a 05 ⋅ =85 ⋅ a 0, so the area of the Koch snowflake is 8/5 of the area of the original triangle. Expressed in terms of the length s of the original triangle this is 2 s 235. The Koch snowflake is self-replicating with six copies around a central point, hence it is an irreptile which is irrep-7. The fractal dimension of the Koch curve is ln 4/ln 3 ≈1.26186 and this is greater than the dimension of a line but less than Peanos space-filling curve. The Koch curve is continuous everywhere but differentiable nowhere and it is possible to tessellate the plane by copies of Koch snowflakes in two different sizes
24.
Sierpinski triangle
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Originally constructed as a curve, this is one of the basic examples of self-similar sets, i. e. it is a mathematically generated pattern that can be reproducible at any magnification or reduction. It is named after the Polish mathematician Wacław Sierpiński, but appeared as a pattern many centuries prior to the work of Sierpiński. There are many different ways of constructing the Sierpinski triangle, the Sierpinski triangle may be constructed from an equilateral triangle by repeated removal of triangular subsets, Start with an equilateral triangle. Subdivide it into four smaller congruent equilateral triangles and remove the central one, repeat step 2 with each of the remaining smaller triangles Each removed triangle is topologically an open set. This process of recursively removing triangles is an example of a subdivision rule. The same sequence of shapes, converging to the Sierpinski triangle, can alternatively be generated by the following steps, the canonical Sierpinski triangle uses an equilateral triangle with a base parallel to the horizontal axis. Shrink the triangle to 1/2 height and 1/2 width, make three copies, and position the three shrunken triangles so that each triangle touches the two triangles at a corner. Note the emergence of the central hole—because the three shrunken triangles can between them cover only 3/4 of the area of the original, repeat step 2 with each of the smaller triangles. Note that this process is not dependent upon the starting shape being a triangle—it is just clearer that way. The first few steps starting, for example, from a square also tend towards a Sierpinski triangle, michael Barnsley used an image of a fish to illustrate this in his paper V-variable fractals and superfractals. The actual fractal is what would be obtained after a number of iterations. More formally, one describes it in terms of functions on closed sets of points. If we let dA denote the dilation by a factor of 1/2 about a point A, then the Sierpinski triangle with corners A, B, and C is the fixed set of the transformation dA ∪ dB ∪ dC. This is a fixed set, so that when the operation is applied to any other set repeatedly. This is what is happening with the triangle above, but any other set would suffice, set vn+1 = 1/2, where rn is a random number 1,2 or 3. Draw the points v1 to v∞, if the first point v1 was a point on the Sierpiński triangle, then all the points vn lie on the Sierpinski triangle. If v1 is outside the triangle, the only way vn will land on the triangle, is if vn is on what would be part of the triangle. Or more simply, Take 3 points in a plane to form a triangle, randomly select any point inside the triangle and consider that your current position
25.
Menger sponge
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In mathematics, a Jerusalem Cube is a fractal object described by Eric Baird in 2011. It is created by recursively drilling Greek cross-shaped holes into a cube, the name comes from a face of the cube resembling a Jerusalem cross pattern. The construction of the Jerusalem Cube can be described as follows, repeat the process on the cubes of rank 1 and 2. Each iteration adds eight cubes of one and twelve cubes of rank two, a twenty-fold increase. Iterating an infinite number of results in the Jerusalem Cube. Dickau, R. Jerusalem Cube Further discussion
26.
Iterated function system
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In mathematics, iterated function systems are a method of constructing fractals, the resulting fractals are often self-similar. IFS fractals, as they are called, can be of any number of dimensions. The fractal is made up of the union of several copies of itself, the canonical example is the Sierpiński gasket, also called the Sierpiński triangle. The functions are normally contractive, which means they bring points closer together, hence, the shape of an IFS fractal is made up of several possibly-overlapping smaller copies of itself, each of which is also made up of copies of itself, ad infinitum. This is the source of its self-similar fractal nature, formally, an iterated function system is a finite set of contraction mappings on a complete metric space. The set S is thus the set of the Hutchinson operator H = ⋃ i =1 N f i. The existence and uniqueness of S is a consequence of the contraction mapping principle, random elements arbitrarily close to S may be obtained by the chaos game, described below. Recently it was shown that the IFSs of noncontractive type can yield attractors and these arise naturally in projective spaces, though classical irrational rotation on the circle can be adapted too. The collection of f i generates a monoid under composition. If there are two such functions, the monoid can be visualized as a binary tree, where, at each node of the tree. In general, if there are k functions, then one may visualize the monoid as a full k-ary tree, sometimes each function f i is required to be a linear, or more generally an affine, transformation, and hence represented by a matrix. However, IFSs may also be built from non-linear functions, including projective transformations, the Fractal flame is an example of an IFS with nonlinear functions. The most common algorithm to compute IFS fractals is called the chaos game and it consists of picking a random point in the plane, then iteratively applying one of the functions chosen at random from the function system to transform the point to get a next point. Each of these algorithms provides a global construction which generates points distributed across the whole fractal, if a small area of the fractal is being drawn, many of these points will fall outside of the screen boundaries. This makes zooming into an IFS construction drawn in this manner impractical, although the theory of IFS requires each function to be contractive, in practice software that implements IFS only require that the whole system be contractive on average. The diagram shows the construction on an IFS from two affine functions, the functions are represented by their effect on the bi-unit square. The combination of the two forms the Hutchinson operator. Three iterations of the operator are shown, and then the image is of the fixed point
27.
Fractal flame
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Fractal flames are a member of the iterated function system class of fractals created by Scott Draves in 1992. Draves open-source code was ported into Adobe After Effects graphics software. Fractal flames differ from ordinary iterated function systems in three ways, Nonlinear functions are iterated in addition to affine transforms, log-density display instead of linear or binary Color by structure instead of monochrome or by density. The tone mapping and coloring are designed to display as much of the detail of the fractal as possible, the algorithm consists of two steps, creating a histogram and then rendering the histogram. First one iterates a set of functions, starting from a chosen point P =. Set of flame functions, { F1, p 1 F2, p 2 … F n, p n In each iteration, then one computes the next iteration of P by applying Fj on. Each individual function has the form, F j = ∑ V k ∈ V a r i a t i o n s w k ⋅ V k where the parameter wk is called the weight of the variation Vk. Draves suggests that all w k, s are non-negative and sum to one, the functions Vk are a set of predefined functions. This is done as follows, The colors in the image will therefore reflect what functions were used to get to that part of the image, to increase the quality of the image, one can use supersampling to decrease the noise. This involves creating a larger than the image so each pixel has multiple data points to pull from. For example, creating a histogram with 300×300 cells in order to draw an 100×100 px image, each pixel would use a 3×3 group of histogram buckets to calculate its value. For each pixel in the image, do the following computations. This is implemented in for example the Apophysis software, to increase the quality even more, one can use gamma correction on each individual color channel, but this is a very heavy computation, since the log function is slow. A simplified algorithm would be to let the brightness be linearly dependent on the frequency, but this would make some parts of the fractal lose detail, which is undesirable. The flame algorithm is like a Monte Carlo simulation, with the flame quality directly proportional to the number of iterations of the simulation, the noise that results from this stochastic sampling can be reduced by blurring the image, to get a smoother result in less time. One does not however want to lose resolution in the parts of the image that receive many samples and this problem can be solved with adaptive density estimation to increase image quality while keeping render times to a minimum. FLAM3 uses a simplification of the methods presented in *Adaptive Filtering for Progressive Monte Carlo Image Rendering*, the idea is to vary the width of the filter inversely proportional to the number of samples available. As a result, areas with few samples and lots of noise get blurred and smoothed, not all Flame implementations use density estimation
28.
L-system
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An L-system or Lindenmayer system is a parallel rewriting system and a type of formal grammar. L-systems were introduced and developed in 1968 by Aristid Lindenmayer, a Hungarian theoretical biologist and botanist at the University of Utrecht, Lindenmayer used L-systems to describe the behaviour of plant cells and to model the growth processes of plant development. L-systems have also used to model the morphology of a variety of organisms. As a biologist, Lindenmayer worked with yeast and filamentous fungi and studied the patterns of various types of algae. Originally the L-systems were devised to provide a description of the development of such simple multicellular organisms. Later on, this system was extended to higher plants. The recursive nature of the L-system rules leads to self-similarity and thereby, plant models and natural-looking organic forms are easy to define, as by increasing the recursion level the form slowly grows and becomes more complex. Lindenmayer systems are popular in the generation of artificial life. L-system grammars are very similar to the semi-Thue grammar, a production consists of two strings, the predecessor and the successor. The rules of the L-system grammar are applied iteratively starting from the initial state, as many rules as possible are applied simultaneously, per iteration. The fact that each iteration employs as many rules as possible differentiates an L-system from a formal language generated by a formal grammar, if the production rules were to be applied only one at a time, one would quite simply generate a language, rather than an L-system. Thus, L-systems are strict subsets of languages, an L-system is context-free if each production rule refers only to an individual symbol and not to its neighbours. Context-free L-systems are thus specified by a context-free grammar, if a rule depends not only on a single symbol but also on its neighbours, it is termed a context-sensitive L-system. If there is one production for each symbol, then the L-system is said to be deterministic. If there are several, and each is chosen with a certain probability during each iteration, using L-systems for generating graphical images requires that the symbols in the model refer to elements of a drawing on the computer screen. For example, the program Fractint uses turtle graphics to produce screen images and it interprets each constant in an L-system model as a turtle command. Lindenmayers original L-system for modelling the growth of algae, /| | |\ |\ \ n=4, A B A A B A B A. into an A one generation later, starting to spawn/repeat/recurse then The result is the sequence of Fibonacci words. If we count the length of string, we obtain the famous Fibonacci sequence of numbers,123581321345589
29.
Polynomial
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In mathematics, a polynomial is an expression consisting of variables and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate x is x2 − 4x +7, an example in three variables is x3 + 2xyz2 − yz +1. Polynomials appear in a variety of areas of mathematics and science. In advanced mathematics, polynomials are used to construct polynomial rings and algebraic varieties, central concepts in algebra, the word polynomial joins two diverse roots, the Greek poly, meaning many, and the Latin nomen, or name. It was derived from the binomial by replacing the Latin root bi- with the Greek poly-. The word polynomial was first used in the 17th century, the x occurring in a polynomial is commonly called either a variable or an indeterminate. When the polynomial is considered as an expression, x is a symbol which does not have any value. It is thus correct to call it an indeterminate. However, when one considers the function defined by the polynomial, then x represents the argument of the function, many authors use these two words interchangeably. It is a convention to use uppercase letters for the indeterminates. However one may use it over any domain where addition and multiplication are defined, in particular, when a is the indeterminate x, then the image of x by this function is the polynomial P itself. This equality allows writing let P be a polynomial as a shorthand for let P be a polynomial in the indeterminate x. A polynomial is an expression that can be built from constants, the word indeterminate means that x represents no particular value, although any value may be substituted for it. The mapping that associates the result of substitution to the substituted value is a function. This can be expressed concisely by using summation notation, ∑ k =0 n a k x k That is. Each term consists of the product of a number—called the coefficient of the term—and a finite number of indeterminates, because x = x1, the degree of an indeterminate without a written exponent is one. A term and a polynomial with no indeterminates are called, respectively, a constant term, the degree of a constant term and of a nonzero constant polynomial is 0. The degree of the polynomial,0, is generally treated as not defined
30.
Newton fractal
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The Newton fractal is a boundary set in the complex plane which is characterized by Newtons method applied to a fixed polynomial p ∈ C or transcendental function. It is the Julia set of the function z ↦ z − p p ′ which is given by Newtons method. When there are no cycles, it divides the complex plane into regions G k, each of which is associated with a root ζ k of the polynomial, k =1, …. In this way the Newton fractal is similar to the Mandelbrot set and it is relevant to numerical analysis because it shows that the Newton method can be very sensitive to its choice of start point. There are even polynomials for which open sets of starting points fail to converge to any root, an example is z 3 −2 z +2. An open set for which the iterations converge towards a given root or cycle, is a Fatou set for the iteration, the complementary set to the union of all these, is the Julia set. The Fatou sets have common boundary, namely the Julia set, therefore each point of the Julia set is a point of accumulation for each of the Fatou sets. It is this property that causes the structure of the Julia set. Additionally or alternatively the colours may be dependent on the distance D, a generalization of Newtons iteration is z n +1 = z n − a p p ′ where a is any complex number. The special choice a =1 corresponds to the Newton fractal, the fixed points of this map are stable when a lies inside the disk of radius 1 centered at 1. When a is outside this disk, the points are locally unstable. If p is a polynomial of n, then the sequence z n is bounded provided that a is inside a disk of radius n centered at n. More generally, Newtons fractal is a case of a Julia set. Julia set Mandelbrot set J. H. Hubbard, D. Schleicher, S. Sutherland, How to Find All Roots of Complex Polynomials by Newtons Method, Inventiones Mathematicae vol
31.
Quaternion
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In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843, a feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a space or equivalently as the quotient of two vectors. Quaternions are generally represented in the form, a + bi + cj + dk where a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units. In practical applications, they can be used other methods, such as Euler angles and rotation matrices, or as an alternative to them. In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, in fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H, or in blackboard bold by H and it can also be given by the Clifford algebra classifications Cℓ0,2 ≅ Cℓ03,0. These rings are also Euclidean Hurwitz algebras, of which quaternions are the largest associative algebra. The unit quaternions can be thought of as a choice of a structure on the 3-sphere S3 that gives the group Spin. Quaternion algebra was introduced by Hamilton in 1843, carl Friedrich Gauss had also discovered quaternions in 1819, but this work was not published until 1900. Hamilton knew that the numbers could be interpreted as points in a plane. Points in space can be represented by their coordinates, which are triples of numbers, however, Hamilton had been stuck on the problem of multiplication and division for a long time. He could not figure out how to calculate the quotient of the coordinates of two points in space. The great breakthrough in quaternions finally came on Monday 16 October 1843 in Dublin, as he walked along the towpath of the Royal Canal with his wife, the concepts behind quaternions were taking shape in his mind. When the answer dawned on him, Hamilton could not resist the urge to carve the formula for the quaternions, i2 = j2 = k2 = ijk = −1, into the stone of Brougham Bridge as he paused on it. On the following day, Hamilton wrote a letter to his friend and fellow mathematician, John T. Graves and this letter was later published in the London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol. xxv, pp 489–95. In the letter, Hamilton states, And here there dawned on me the notion that we must admit, in some sense, an electric circuit seemed to close, and a spark flashed forth. Hamilton called a quadruple with these rules of multiplication a quaternion, Hamiltons treatment is more geometric than the modern approach, which emphasizes quaternions algebraic properties
32.
Fractal landscape
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A fractal landscape is a surface generated using a stochastic algorithm designed to produce fractal behaviour that mimics the appearance of natural terrain. In other words, the result of the procedure is not a deterministic fractal surface, many natural phenomena exhibit some form of statistical self-similarity that can be modeled by fractal surfaces. The modeling of the Earths rough surfaces via fractional Brownian motion was first proposed by Benoît Mandelbrot, the first use of a fractal-generated landscape in a film was in 1982 for the movie Star Trek II, The Wrath of Khan. Loren Carpenter refined the techniques of Mandelbrot to create an alien landscape, whether or not natural landscapes behave in a generally fractal manner has been the subject of some research. Technically speaking, any surface in space has a topological dimension of 2. Real landscapes however, have varying behaviour at different scales and this means that an attempt to calculate the overall fractal dimension of a real landscape can result in measures of negative fractal dimension, or of fractal dimension above 3. In particular, many studies of phenomena, even those commonly thought to exhibit fractal behaviour. For instance, Richardsons examination of the coastline of Britain showed fractal behaviour of the coastline over only two orders of magnitude. In general, there is no reason to suppose that the processes that shape terrain on large scales exhibit the same mathematical behaviour as those that shape terrain on smaller scales. Real landscapes also have varying statistical behaviour from place to place, a fractal function, however, is statistically stationary, meaning that its bulk statistical properties are the same everywhere. Thus, any real approach to modeling landscapes requires the ability to modulate fractal behaviour spatially, additionally real landscapes have very few natural minima, whereas a fractal function has as many minima as maxima, on average. Real landscapes also have features originating with the flow of water and ice over their surface and it is because of these considerations that the simple fractal functions are often inappropriate for modeling landscapes. The process is repeated on the four new squares, and so on, there are many fractal procedures capable of creating terrain data, however, the term fractal landscape has become more generic. Brownian surface Bryce Diamond-square algorithm Grome Outerra Terragen Octree Quadtree Lewis, is the Fractal Model Appropriate for Terrain. Van Lawick van Pabst, Joost, Jense, Hans, dynamic Terrain Generation Based on Multifractal Techniques. A Web-Wide World by Ken Perlin,1998, a Java applet showing a sphere with a generated landscape
33.
Jackson Pollock
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Paul Jackson Pollock, known professionally as Jackson Pollock, was an American painter and a major figure in the abstract expressionist movement. He was well known for his style of drip painting. During his lifetime, Pollock enjoyed considerable fame and notoriety, he was a major artist of his generation, regarded as reclusive, he had a volatile personality, and struggled with alcoholism for most of his life. In 1945, he married the artist Lee Krasner, who became an important influence on his career, Pollock died at the age of 44 in an alcohol-related single-car accident when he was driving. In December 1956, four months after his death, Pollock was given a retrospective exhibition at the Museum of Modern Art in New York City. A larger, more comprehensive exhibition of his work was held there in 1967, in 1998 and 1999, his work was honored with large-scale retrospective exhibitions at MoMA and at The Tate in London. Pollock was born in Cody, Wyoming, in 1912, the youngest of five sons and his parents, Stella May and LeRoy Pollock, were born and grew up in Tingley, Iowa and were educated at Tingley High School. Pollocks mother is interred at Tingley Cemetery, Ringgold County, Iowa and his father had been born with the surname McCoy, but took the surname of his adoptive parents, neighbors who adopted him after his own parents had died within a year of each other. Stella and LeRoy Pollock were Presbyterian, they were of Irish and Scots-Irish descent, LeRoy Pollock was a farmer and later a land surveyor for the government, moving for different jobs. Stella, proud of her familys heritage as weavers, made, in November 1912, Stella took her sons to San Diego, Jackson was just 10 months old and would never return to Cody. He subsequently grew up in Arizona and Chico, California, while living in Echo Park, California, he enrolled at Los Angeles Manual Arts High School, from which he was expelled. He had already been expelled in 1928 from another high school, during his early life, Pollock explored Native American culture while on surveying trips with his father. In 1930, following his older brother Charles Pollock, he moved to New York City, bentons rural American subject matter had little influence on Pollocks work, but his rhythmic use of paint and his fierce independence were more lasting. In the early 1930s, Pollock spent a summer touring the Western United States together with Glen Rounds, an art student. Pollock was introduced to the use of paint in 1936 at an experimental workshop in New York City by the Mexican muralist David Alfaro Siqueiros. He later used paint pouring as one of techniques on canvases of the early 1940s, such as Male and Female. After his move to Springs, he began painting with his canvases laid out on the studio floor, from 1938 to 1942 Pollock worked for the WPA Federal Art Project. Henderson engaged him through his art, encouraging Pollock to make drawings, jungian concepts and archetypes were expressed in his paintings
34.
Fractal dimension
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In that paper, Mandelbrot cited previous work by Lewis Fry Richardson describing the counter-intuitive notion that a coastlines measured length changes with the length of the measuring stick used. In terms of that notion, the dimension of a coastline quantifies how the number of scaled measuring sticks required to measure the coastline changes with the scale applied to the stick. There are several formal definitions of fractal dimension that build on this basic concept of change in detail with change in scale. One non-trivial example is the dimension of a Koch snowflake. It has a dimension of 1, but it is by no means a rectifiable curve. No small piece of it is line-like, but rather is composed of a number of segments joined at different angles. The fractal dimension of a curve can be explained intuitively thinking of a line as an object too detailed to be one-dimensional. Therefore its dimension might best be described not by its usual topological dimension of 1 but by its fractal dimension, a fractal dimension is an index for characterizing fractal patterns or sets by quantifying their complexity as a ratio of the change in detail to the change in scale. Several types of dimension can be measured theoretically and empirically. Fractal dimensions were first applied as an index characterizing complicated geometric forms for which the details seemed more important than the gross picture, for sets describing ordinary geometric shapes, the theoretical fractal dimension equals the sets familiar Euclidean or topological dimension. Thus, it is 0 for sets describing points,1 for sets describing lines,2 for sets describing surfaces, but this changes for fractal sets. If the theoretical fractal dimension of a set exceeds its topological dimension, the set is considered to have fractal geometry. Similarly, a surface with fractal dimension of 2.1 fills space very much like an ordinary surface, the relationship of an increasing fractal dimension with space-filling might be taken to mean fractal dimensions measure density, but that is not so, the two are not strictly correlated. Instead, a fractal dimension measures complexity, a related to certain key features of fractals, self-similarity. These features are evident in the two examples of fractal curves, both are curves with topological dimension of 1, so one might hope to be able to measure their length or slope, as with ordinary lines. But we cannot do either of these things, because fractal curves have complexity in the form of self-similarity, the self-similarity lies in the infinite scaling, and the detail in the defining elements of each set. The length between any two points on curves is undefined because the curves are theoretical constructs that never stop repeating themselves. Every smaller piece is composed of a number of scaled segments that look exactly like the first iteration
35.
Electric Sheep
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Electric Sheep is a distributed computing project for animating and evolving fractal flames, which are in turn distributed to the networked computers, which display them as a screensaver. The process is transparent to the user, who can simply install the software as a screensaver. As the screensaver entertains the user, their computer is used for rendering commercial projects. There are about 500,000 active users, according to Mitchell Whitelaw in his Metacreation, Art and Artificial Life, On the screen they are luminous, twisting, elastic shapes, abstract tangles and loops of glowing filaments. The name Electric Sheep is taken from the title of Philip K. Dicks novel Do Androids Dream of Electric Sheep, the title mirrors the nature of the project, computers who have started running the screensaver begin rendering the fractal movies. Users may vote on sheep that they like or dislike, each movie is a fractal flame with several of its parameters animated. Both are automatically downloaded by the screen saver, the underlying copyright issues raised by generative, distributed digital art projects involve novel legal issues that the current copyright system can not understand or handle. The screensaver was created and released as free software by Scott Draves in 1999 and continues to be developed by him, the 2.7. x series differs from the old versions. It has a new logo, higher quality sheep and other features and it has switched to a freemium model in which the server software is not available and much of the computed data is not available under a free license, which led to its removal from Debian
36.
Distributed computing
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Distributed computing is a field of computer science that studies distributed systems. A distributed system is a model in which components located on networked computers communicate and coordinate their actions by passing messages, the components interact with each other in order to achieve a common goal. Three significant characteristics of distributed systems are, concurrency of components, lack of a global clock, examples of distributed systems vary from SOA-based systems to massively multiplayer online games to peer-to-peer applications. A computer program that runs in a system is called a distributed program. There are many alternatives for the message passing mechanism, including pure HTTP, RPC-like connectors, Distributed computing also refers to the use of distributed systems to solve computational problems. In distributed computing, a problem is divided into many tasks, each of which is solved by one or more computers, which communicate with each other by message passing. The terms are used in a much wider sense, even referring to autonomous processes that run on the same physical computer. The entities communicate with each other by message passing, a distributed system may have a common goal, such as solving a large computational problem, the user then perceives the collection of autonomous processors as a unit. Other typical properties of distributed systems include the following, The system has to tolerate failures in individual computers. The structure of the system is not known in advance, the system may consist of different kinds of computers and network links, each computer has only a limited, incomplete view of the system. Each computer may know one part of the input. Distributed systems are groups of networked computers, which have the goal for their work. The terms concurrent computing, parallel computing, and distributed computing have a lot of overlap, the same system may be characterized both as parallel and distributed, the processors in a typical distributed system run concurrently in parallel. Parallel computing may be seen as a tightly coupled form of distributed computing. In distributed computing, each processor has its own private memory, Information is exchanged by passing messages between the processors. The figure on the right illustrates the difference between distributed and parallel systems, figure shows a parallel system in which each processor has a direct access to a shared memory. The situation is complicated by the traditional uses of the terms parallel and distributed algorithm that do not quite match the above definitions of parallel. The use of concurrent processes that communicate by message-passing has its roots in operating system architectures studied in the 1960s, the first widespread distributed systems were local-area networks such as Ethernet, which was invented in the 1970s
37.
Screensaver
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A screensaver is a computer program that blanks the screen or fills it with moving images or patterns when the computer is not in use. Initially designed to prevent phosphor burn-in on CRT and plasma monitors, screensavers are now used primarily for entertainment. Decades before the first computers using this technology were invented, Robert A, many modern television operating systems, media players and other digital entertainment systems include optional screensavers. Some screensavers also offer functions like automated workstation password protection during inactivity or disk scan with installed antivirus software. Before the advent of LCD screens, most computer screens were based on cathode ray tubes, cathode ray televisions, oscilloscopes and other devices that use CRTs are all susceptible to phosphor burn-in, as are plasma displays to some extent. Screen-saver programs were designed to avoid these effects by automatically changing the images on the screen during periods of user inactivity. For CRTs used in public, such as ATMs and railway ticketing machines, blanking the screen is out of the question as the machine would appear to be out of service. In these applications, burn-in can be prevented by shifting the position of the display contents every few seconds, LCD computer monitors, including the display panels used in laptop computers, are not susceptible to burn-in because the image is not directly produced by phosphors. For these reasons, screensavers today are primarily for decorative/entertainment purposes and they usually feature moving images or patterns and sometimes sound effects. One increasingly popular application is for screensavers to activate a useful background task and this allows applications to use resources only when the computer would be otherwise idle. The first screensaver was allegedly written for the original IBM PC by John Socha, best known for creating the Norton Commander, the screensaver, named scrnsave, was published in the December 1983 issue of the Softalk magazine. It simply blanked the screen three minutes of inactivity. The first screensaver that allowed users to change the time was released on Apples Lisa. The Atari 400 and 800s screens would also go through random screensaver-like color changes if they were left inactive for too long, the user had no control over this. These computers, released in 1979, are technically earlier screen savers, and prior to these computers, the 1977 Atari VCS/2600 gaming console included color cycling in games like Combat or Breakout, in order to prevent burn-in of game images to 1970s-era televisions. In addition, the first model of the TI-30 calculator from 1976 featured a screensaver and this was chiefly used to save battery power, as the LED display was more power intensive than later LCD models. These are examples of screensavers in ROM or the firmware of a computer, today with the help of modern graphics technologies there is a wide variety of screensavers. Because of 3D computer graphics, which provide realistic environments, 3D screensavers are available, screensavers are usually designed and coded using a variety of programming languages as well as graphics interfaces
38.
Art
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In their most general form these activities include the production of works of art, the criticism of art, the study of the history of art, and the aesthetic dissemination of art. The oldest documented forms of art are visual arts, which include creation of images or objects in fields including painting, sculpture, printmaking, photography, and other visual media. Music, theatre, film, dance, and other performing arts, as well as literature, until the 17th century, art referred to any skill or mastery and was not differentiated from crafts or sciences. Art may be characterized in terms of mimesis, expression, communication of emotion, during the Romantic period, art came to be seen as a special faculty of the human mind to be classified with religion and science. Though the definition of what art is disputed and has changed over time, general descriptions mention an idea of imaginative or technical skill stemming from human agency. The nature of art, and related such as creativity. One early sense of the definition of art is related to the older Latin meaning. English words derived from this meaning include artifact, artificial, artifice, medical arts, however, there are many other colloquial uses of the word, all with some relation to its etymology. Several dialogues in Plato tackle questions about art, Socrates says that poetry is inspired by the muses, and is not rational. He speaks approvingly of this, and other forms of divine madness in the Phaedrus, and yet in the Republic wants to outlaw Homers great poetic art, in Ion, Socrates gives no hint of the disapproval of Homer that he expresses in the Republic. For example, music imitates with the media of rhythm and harmony, whereas dance imitates with rhythm alone, the forms also differ in their object of imitation. Comedy, for instance, is an imitation of men worse than average. Lastly, the forms differ in their manner of imitation—through narrative or character, through change or no change, Aristotle believed that imitation is natural to mankind and constitutes one of mankinds advantages over animals. The second, and more recent, sense of the art as an abbreviation for creative art or fine art emerged in the early 17th century. The creative arts are a collection of disciplines which produce artworks that are compelled by a drive and convey a message, mood. Art is something that stimulates an individuals thoughts, emotions, beliefs, works of art can be explicitly made for this purpose or interpreted on the basis of images or objects. Often, if the skill is being used in a common or practical way, likewise, if the skill is being used in a commercial or industrial way, it may be considered commercial art instead of fine art. On the other hand, crafts and design are considered applied art
39.
Pattern
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A pattern, apart from the terms use to mean Template, is a discernible regularity in the world or in a manmade design. As such, the elements of a repeat in a predictable manner. A geometric pattern is a kind of pattern formed of geometric shapes, any of the senses may directly observe patterns. Conversely, abstract patterns in science, mathematics, or language may be only by analysis. Direct observation in practice means seeing visual patterns, which are widespread in nature, visual patterns in nature are often chaotic, never exactly repeating, and often involve fractals. Natural patterns include spirals, meanders, waves, foams, tilings, cracks, Patterns have an underlying mathematical structure, indeed, mathematics can be seen as the search for regularities, and the output of any function is a mathematical pattern. Similarly in the sciences, theories explain and predict regularities in the world, in art and architecture, decorations or visual motifs may be combined and repeated to form patterns designed to have a chosen effect on the viewer. In computer science, a design pattern is a known solution to a class of problems in programming. In fashion, the pattern is a used to create any number of similar garments. Nature provides examples of many kinds of pattern, including symmetries, trees and other structures with a dimension, spirals, meanders, waves, foams, tilings, cracks. Symmetry is widespread in living things, animals that move usually have bilateral or mirror symmetry as this favours movement. Plants often have radial or rotational symmetry, as do many flowers, as well as animals which are largely static as adults, fivefold symmetry is found in the echinoderms, including starfish, sea urchins, and sea lilies. Among non-living things, snowflakes have striking sixfold symmetry, each flake is unique, crystals have a highly specific set of possible crystal symmetries, they can be cubic or octahedral, but cannot have fivefold symmetry. Many natural patterns are shaped by this apparent randomness, including vortex streets, waves are disturbances that carry energy as they move. Mechanical waves propagate through a medium – air or water, making it oscillate as they pass by, wind waves are surface waves that create the chaotic patterns of the sea. As they pass over sand, such waves create patterns of ripples, similarly, as the passes over sand. Foams obey Plateaus laws, which films to be smooth and continuous. Foam and bubble patterns occur widely in nature, for example in radiolarians, sponge spicules, cracks form in materials to relieve stress, with 120 degree joints in elastic materials, but at 90 degrees in inelastic materials
40.
Chaos theory
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Chaos theory is a branch of mathematics focused on the behavior of dynamical systems that are highly sensitive to initial conditions. This happens even though these systems are deterministic, meaning that their behavior is fully determined by their initial conditions. In other words, the nature of these systems does not make them predictable. This behavior is known as chaos, or simply chaos. The theory was summarized by Edward Lorenz as, Chaos, When the present determines the future, Chaotic behavior exists in many natural systems, such as weather and climate. It also occurs spontaneously in some systems with components, such as road traffic. This behavior can be studied through analysis of a mathematical model, or through analytical techniques such as recurrence plots. Chaos theory has applications in several disciplines, including meteorology, sociology, physics, environmental science, computer science, engineering, economics, biology, ecology, the theory formed the basis for such fields of study as complex dynamical systems, edge of chaos theory, self-assembly process. Chaos theory concerns deterministic systems whose behavior can in principle be predicted, Chaotic systems are predictable for a while and then appear to become random. Some examples of Lyapunov times are, chaotic electrical circuits, about 1 millisecond, weather systems, a few days, in chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast and this means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random, in common usage, chaos means a state of disorder. However, in theory, the term is defined more precisely. Although no universally accepted mathematical definition of chaos exists, a commonly used definition originally formulated by Robert L, in these cases, while it is often the most practically significant property, sensitivity to initial conditions need not be stated in the definition. If attention is restricted to intervals, the second property implies the other two, an alternative, and in general weaker, definition of chaos uses only the first two properties in the above list. Sensitivity to initial conditions means that each point in a system is arbitrarily closely approximated by other points with significantly different future paths. Thus, a small change, or perturbation, of the current trajectory may lead to significantly different future behavior. C. Entitled Predictability, Does the Flap of a Butterflys Wings in Brazil set off a Tornado in Texas, the flapping wing represents a small change in the initial condition of the system, which causes a chain of events leading to large-scale phenomena
41.
Chinese painting
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Chinese painting is one of the oldest continuous artistic traditions in the world. Painting in the style is known today in Chinese as guóhuà, meaning national or native painting. Traditional painting involves essentially the same techniques as calligraphy and is done with a brush dipped in ink or coloured pigments. As with calligraphy, the most popular materials on which paintings are made are paper, the finished work can be mounted on scrolls, such as hanging scrolls or handscrolls. Traditional painting can also be done on album sheets, walls, lacquerware, folding screens, the two main techniques in Chinese painting are, Gongbi, meaning meticulous, uses highly detailed brushstrokes that delimits details very precisely. It is often coloured and usually depicts figural or narrative subjects. It is often practised by artists working for the court or in independent workshops. Ink and wash painting, in Chinese shui-mo also loosely termed watercolour or brush painting and this style is also referred to as xieyi or freehand style. Landscape painting was regarded as the highest form of Chinese painting, the time from the Five Dynasties period to the Northern Song period is known as the Great age of Chinese landscape. In the south, Dong Yuan, Juran, and other artists painted the rolling hills and rivers of their native countryside in peaceful scenes done with softer and these two kinds of scenes and techniques became the classical styles of Chinese landscape painting. Chinese painting and calligraphy distinguish themselves from other arts by emphasis on motion. The practice is traditionally first learned by rote, in which the shows the right way to draw items. The apprentice must copy these items strictly and continuously until the movements become instinctive, in contemporary times, debate emerged on the limits of this copyist tradition within modern art scenes where innovation is the rule. Changing lifestyles, tools, and colors are also influencing new waves of masters, the earliest paintings were not representational but ornamental, they consisted of patterns or designs rather than pictures. Early pottery was painted with spirals, zigzags, dots, or animals and it was only during the Warring States period that artists began to represent the world around them. Calligraphy and painting were thought to be the purest forms of art, the implements were the brush pen made of animal hair, and black inks made from pine soot and animal glue. In ancient times, writing, as well as painting, was done on silk, however, after the invention of paper in the 1st century AD, silk was gradually replaced by the new and cheaper material. Original writings by famous calligraphers have been valued throughout Chinas history and are mounted on scrolls
42.
Penjing
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Shānshuǐ pénjǐng, Landscape penjing that depicts a miniature landscape by carefully selecting and shaping rocks, which are usually placed in a container in contact with water. Small live plants are placed within the composition to complete the depiction, shuǐhàn pénjǐng, A water and land penjing style that effectively combines the first two, including miniature trees and optionally miniature figures and structures to portray a landscape in detail. Similar practices exist in other cultures, including the Japanese traditions of bonsai and saikei, generally speaking, tree penjing specimens differ from bonsai by allowing a wider range of tree shapes and by planting them in bright-colored and creatively shaped pots. In contrast, bonsai are more simplified in shape with larger-in-proportion trunks, while saikei depicts living landscapes in containers, like water and land penjing, it does not use miniatures to decorate the living landscape. Hòn non bộ focuses on depicting landscapes of islands and mountains, usually in contact with water, like water and land penjing, hòn non bộ specimens can feature miniature figures, vehicles, and structures. Classical Chinese gardens often contain arrangements of miniature trees and rockeries known as penjing and these creations of carefully pruned trees and rocks are small-scale renditions of natural landscapes. They are often referred to as living sculptures or as three-dimensional poetry and their artistic composition captures the spirit of nature and distinguishes them from ordinary potted plants. The container known as the pen originated in Neolithic China in the Yangshao culture as a shallow dish with a foot. It was later one of the vessels manufactured in bronze for use in ceremonies and religious rituals during the Shang dynasty. When foreign trade introduced into China new herbal aromatics in the 2nd century BC, smaller versions of the pen dish were sometimes used as bottom pieces either to catch hot embers or to be filled with water to represent the ocean out of which the sacred mountains/islands arose. Since at least the 1st century AD, Daoist mysticism has included the recreating of magical sites in miniature to focus, also, floral altar decorations were introduced and floral designs started to become a dominant force in Chinese art. Five centuries later the Chán school of Buddhism was established, in which renewed Indian dhyana Buddhist teachings were merged with native Chinese Daoism, Chán maintained its more active, vital spirit even as other Buddhist sects were becoming more rigidly formalized. The earliest-known graphic dates from 706 and is found in a mural on a corridor leading to the tomb of Prince Zhang Huai at the Qianling Mausoleum site. Excavated in 1972, the show two maid servants carrying penjing with miniature rockeries and fruit trees. The first highly prized trees are believed to have collected in the wild and were full of twists, knots. These were seen as sacred, of no practical value for timber or other ordinary purpose. These naturally dwarfed plants were held to be endowed with special concentrated energies due to age, the viewpoint of Chán Buddhism would continue to impact the creation of miniature landscapes. Smaller and younger plants which could be collected closer to civilization, horticultural techniques to increase the appearance of age by emphasizing trunk, root, and branch size, texture, and shapes would eventually be employed with these specimens
