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| [[File:Selimiye Mosque, Dome.jpg|thumb|The interior side view of the main dome of [[Selimiye Mosque (Edirne)|Selimiye Mosque]] in [[Edirne]], Turkey, which contains some [[self-similar]] patterns]]
| | The author is known by the name of Figures Lint. Years ago we moved to North Dakota. Hiring is my occupation. Doing ceramics is what my family and I enjoy.<br><br>Feel free to surf to my web site: [http://www.hotporn123.com/blog/150887 www.hotporn123.com] |
| [[Image:Julian fractal.jpg|thumb|A piece generated in [[Apophysis (software)|Apophysis]]]]
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| [[File:NonIntegerMultibrot - Breaking of Space.jpg|thumb|right|A detail from a non-integer [[Multibrot set]]]]
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| [[File:FWF Samuel Monnier détail.jpg|thumb|A [[Fibonacci word]] fractal]]
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| '''Fractal art''' is a form of [[algorithmic art]] created by calculating [[fractal]] objects and representing the calculation results as still images, animations, and [[Algorithmic composition|media]]. Fractal art developed from the mid-1980s onwards.<ref name="fgad">{{cite book |title=Fractal geometry in architecture and design |last=Bovill |first=Carl |year=1996 |publisher=Birkhauser |location=Boston |isbn=0-8176-3795-8 |page=153 |url=http://books.google.com/books?id=w5ptaiGsac4C |accessdate=28 October 2011}}</ref> It is a genre of [[computer art]] and [[digital art]] which are part of [[new media art]]. The [[Julia set]] and [[Mandelbrot set]]s can be considered as [[icon]]s of fractal art.<ref name="hema">{{cite book |title=The heart of mathematics: an invitation to effective thinking |last=Burger |first=Edward B. |coauthors=Michael P. Starbird |year=2005 |publisher=Springer |isbn=1-931914-41-9 |page=475 |url=http://books.google.com/books?id=M-qK8anbZmwC |accessdate=30 October 2011}}</ref>
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| Fractal art (especially in the western world) is not drawn or painted by hand. It is usually created indirectly with the assistance of [[fractal-generating software]], iterating through three phases: setting parameters of appropriate fractal software; executing the possibly lengthy calculation; and evaluating the product. In some cases, other [[graphics software|graphics programs]] are used to further modify the images produced. This is called post-processing. Non-fractal imagery may also be integrated into the artwork.<ref name="mra">{{cite web |url=http://www.casperjournal.com/article_bbe58a64-0b86-5e64-8fc5-459eafbe67fb.html |title=Meet Reginald Atkins, mathematical artist |author=Elysia Conner |date=February 25, 2009 |publisher=CasperJournal.com |accessdate=October 28, 2011 }}</ref>
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| It was assumed that Fractal art could not have developed without computers because of the [[calculation|calculative]] capabilities they provide.<ref name="dima">{{cite book |title=Digital Mantras: The languages of abstract and virtual worlds |last=Steven R. |first=Holtzman |year=1995 |publisher=MIT Press |isbn=0-262-58143-4 |page=241 |url=http://books.google.com/books?id=gc5hnRuABy0C |accessdate=28 October 2011}}</ref> Fractals are generated by applying [[Iteration|iterative]] methods to solving non-linear equations or [[polynomial equation]]s. Fractals are any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size.<ref>[http://www.merriam-webster.com/dictionary/fractal Fractal - Definition]. Free Merriam-Webster Dictionary.</ref>
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| ==Types==
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| [[File:Mandelbulb072a.JPG|thumb|A 3D [[Mandelbulb]] fractal generated using Visions of Chaos]]
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| There are many different kinds of fractal images and can be subdivided into several groups.
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| * Fractals derived from standard geometry by using iterative transformations on an initial common figure like a straight line (the Cantor dust or the [[Koch snowflake|von Koch curve]]), a triangle (the [[Sierpinski triangle]]), or a cube (the [[Menger sponge]]). The first fractal figures invented near the end of the 19th and early 20th centuries belong to this group.
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| * IFS ([[iterated function systems]])
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| * [[Strange attractors]]
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| * [[Flame fractals|Fractal flame]]
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| * [[L-system]] fractals
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| * Fractals created by the iteration of complex [[polynomial]]s: perhaps the most famous fractals.
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| * [[Newton fractal]]s, including [[Nova fractal]]s
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| * [[Quaternionic]] and (recently) hypernionic{{clarify||date=January 2014}} fractals <ref>[http://paulbourke.net/fractals/quatjulia/ Quaternion Julia Fractals]</ref>
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| * [[Fractal terrain]]s generated by random fractal processes<ref>[https://www.fractalus.com/fractal-art-faq/faq03.html#3a Fractal Art FAQ]</ref>
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| * [[Mandelbulb]]s are a kind of three dimensional fractal.
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| Fractal expressionism is a term used to differentiate traditional visual art that incorporates fractal elements such as [[self-similarity]] for example. Perhaps the best example of fractal expressionism is found in [[Jackson Pollock]]'s dripped patterns. They have been analysed and found to contain a [[fractal dimension]] which has been attributed to his technique.<ref name="coex">{{cite book |title=Complexity explained |last=Érdi |first=Péter |year=2008 |publisher=Springer |isbn=3-540-35777-7 |page=214 |url=http://books.google.com/books?id=JwgpLvknc8wC |accessdate=29 October 2011}}</ref>
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| ==Techniques==
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| [[File:Electricsheep-14525.jpg|thumb|Fractal image generated by [[Electric Sheep]]]]
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| [[File:Sterling2 4728aa.jpg|thumb|A fractal image made with [[Sterling (program)|Sterling]]]]
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| Fractals of all kinds have been used as the basis for digital art and animation. High resolution color graphics became increasingly available at scientific research labs in the mid-1980s. Scientific forms of art, including fractal art, have developed separately from [[mainstream]] culture.<ref name="ciem">{{cite book |title=Critical issues in electronic media |last=Penny |first=Simon |year=1995 |publisher=State University of New York Press |isbn=0-7914-2317-4 |pages=81–82 |url=http://books.google.com/books?id=vzFJnyBjaLMC |accessdate=29 October 2011}}</ref> Starting with 2-dimensional details of fractals, such as the Mandelbrot Set, fractals have found artistic application in fields as varied as texture generation, plant growth simulation and landscape generation.
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| Fractals are sometimes combined with human-assisted [[evolutionary algorithms]], either by iteratively choosing good-looking specimens in a set of random variations of a fractal artwork and producing new variations, to avoid dealing with cumbersome or unpredictable parameters, or collectively, as in the [[Electric Sheep]] project, where people use [[fractal flame]]s rendered with [[distributed computing]] as their [[screensaver]] and "rate" the flame they are viewing, influencing the server, which reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.
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| Many fractal images are admired because of their perceived [[Principles of art#Harmony|harmony]]. This is typically achieved by the [[pattern]]s which emerge from the [[Principles of art#Balance|balance]] of order and [[Chaos theory|chaos]]. Similar qualities have been described in [[Chinese painting]] and [[Penjing|miniature trees and rockeries]].<ref name="caftc">{{cite book |title=Chaos, complexity, curriculum and culture |editor1-first=William E. |editor1-last=Doll, Jr |editor2-first=Jayne |editor2-last=Fleener |editor3-first=Donna |editor3-last=Trueit |editor4-first=John |editor4-last=St. Julien |last=Wang |first=Hongyu |chapter=Chinese aesthetics, Fractals and the Tao of Curriculum |year=2005 |publisher=Peter Lang Publishing |location=New York |isbn=978-0-8204-6780-1 |page=301 |url=http://books.google.com/books?id=fROt7Yjz3xgC |accessdate=28 October 2011}}</ref>
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| Fractal rendering programs used to make fractal art include [[Ultra Fractal]], [[Apophysis (software)|Apophysis]], [[Bryce (software)|Bryce]] and [[Sterling (program)|Sterling]]. [[Fractint]] was the first widely used fractal generating program.{{cn|date=November 2013}}
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| ==Landscapes==
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| [[Image:Mandelbrot island.jpg|thumb|right|A 3D landscape generated with [[Terragen]]]]
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| {{main|Fractal landscape}}
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| The first fractal image that was intended to be a work of art was probably the famous one on the cover of ''[[Scientific American]]'', August 1985. This image showed a [[landscape]] formed from the potential function on the domain outside the (usual) [[Mandelbrot set]]. However, as the potential function grows fast near the boundary of the Mandelbrot set, it was necessary for the creator to let the landscape grow downwards, so that it looked as if the Mandelbrot set was a [[plateau]] atop a mountain with steep sides. The same technique was used a year after in some images in ''[[The Beauty of Fractals]]'' by [[Heinz-Otto Peitgen]] and [[Michael M. Richter]].
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| In this book you can find a formula to estimate the distance from a point outside the Mandelbrot set to the boundary of the Mandelbrot set (and a similar formula for the Julia sets), and one can wonder why the creator did not use this function instead of the potential function, because it grows in a more natural way (see the formula in the articles [[Mandelbrot set]] and [[Julia set]]).
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| The three pictures show landscapes formed from the distance function for a family of iterations of the form <math>z^{2} + az^{4} + c</math>. If, in a light from the sun. Then we imagine the rays are parallel (and given by two angles), and we let the colour of a point on the surface be determined by the angle between this direction and the slope of the surface at the point. The intensity (on the earth) is independent of the distance, but the light grows whiter because of the atmosphere, and sometimes the ground looks as if it is enveloped in a veil of mist (second picture). We can also let the light be "artificial", as if it issues from a lantern held by the observer. In this case the colour must grow darker with the distance (third picture).
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| ==Artists==
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| The British artist [[William Latham (computer scientist)|William Latham]], has used fractal geometry and other computer graphics techniques in his works.<ref name="fpc">{{cite book |title=Fractals: The Patterns of Chaos |last=Briggs |first=John |authorlink=John Briggs (author) |year=1992 |publisher=Thames and Hudson |location=London |isbn=0-500-27693-5 |page=169 }}</ref> [[Greg Sams]] has used fractal designs in postcards, t-shirts and textiles. American [[Vicky Brago-Mitchell]] has created fractal art which has appeared in exhibitions and on magazine covers. [[Scott Draves]] is credited with inventing flame fractals. [[Carlos Ginzburg]] has explored fractal art and developed a concept called "homo fractalus" which is based around the idea that the human is the ultimate fractal.<ref name="cagi">{{cite web |url=http://muse.jhu.edu/journals/leonardo/v034/34.1ginzburg.html |title=Carlos Ginzburg |year=2001 |work=Leonardo |publisher=International Society for the Arts, Sciences and Technology |accessdate=29 October 2011 }}</ref> Merrin Parkers from New Zealand specialises in fractal art.<ref name="hfn">{{cite book |title=Heaven's fractal net: retrieving lost visions in the humanities, Volume 1 |last=Jackson |first=William Joseph |year=2004 |publisher=Indiana University Press |isbn=0-253-21620-6 |page=116 |url=http://books.google.com/books?id=U0rJz7FC2z8C |accessdate=30 October 2011}}</ref>
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| ==Exhibits==
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| Fractal art has been exhibited at major international art galleries.<ref name="aue">{{cite book |title=The artful universe expanded |last=Barrow |first=John D. |authorlink=John D. Barrow |year=1995 |publisher=Oxford University Press |isbn=0-19-280569-X |page=69 |url=http://books.google.com/books?id=sXQJbl5mamcC |accessdate=28 October 2011}}</ref> One of the first exhibitions of fractal art was "Map Art", a travelling exhibition of works from researchers at the [[University of Bremen]].<ref name="funa">{{cite book |title=FutureNatural |last=Robertson |first=George |year=1996 |publisher=Routledge |location=London |isbn=0-415-07013-9 |pages=220–221 |url=http://books.google.com/books?id=zby751yKI_kC |accessdate=28 October 2011}}</ref> Mathematicians [[Heinz-Otto Peitgen]] and [[Michael M. Richter]] discovered that the public not only found the images aesthetically pleasing but that they also wanted to understand the scientific background to the images.<ref name="asc">{{cite web |url=http://www.uiowa.edu/~commstud/resources/digitalmedia/wright.html |title=Art and Science in Chaos: Contesting Readings of Scientific Visualisation |author=Richard Wright |work=ISEA'94 Proceedings - The Next Generation |publisher=University of Iowa |accessdate=28 October 2011 }}</ref>
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| In 1989, fractals were part of the subject matter for an art show called ''Strange Attractors: Signs of Chaos'' at the [[New Museum of Contemporary Art]].<ref name="ciem"/> The show consisted of photographs, installations and sculptures designed to provide greater scientific [[discourse]] to the field which had already captured the public's attention through colourful and intricate computer imagery.
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| ==See also==
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| {{Portal|Visual arts|Computer graphics|Computer Science|Mathematics}}
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| * [[Mathematics and art]]
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| * [[Orbit trap]]
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| * [[Systems art]]
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| * [[Persian carpet]]
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| {{-}}
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| ==References==
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| {{Reflist|2}}
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| ==Further reading==
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| * {{cite book|first=Clifford|last=Pickover|authorlink=Clifford A. Pickover|title=Computers, Pattern, Chaos and Beauty|isbn=0-486-41709-3}}
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| * {{cite book|first=Manfred|last=Schroeder|title=Fractals, Chaos, Power Laws|isbn=0-7167-2357-3}}
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| * Michelitsch, Michael; Rössler, Otto E. The "Burning Ship" and Its Quasi-Julia Sets, Computers & Graphics Vol. 16, No. 4, pp. 435–438, 1992.
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| * Michelitsch, Michael; Rössler, Otto E. "A New Feature in Hénon's Map." Computers & Graphics Vol. 13, No. 2, pp. 263––265, 1989.
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| * [http://www.springerlink.com/content/p5p15267t7l11h07 Wondering angels of Fractal arts]
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| ==External links==
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| {{Commons category|Fractal art}}
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| * {{dmoz|Science/Math/Chaos_and_Fractals/Fractal_art/|Fractal Art}}
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| * [[commons:Mandelbrot set#Some details of the Mandelbrot set|Art and the Mandelbrot set (in commons.Wikimedia)]]
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| * [[commons:Fractal|Fractals in Wikimedia]]
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| [[Category:Fractals]]
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| [[Category:Abstract art]]
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