Fractal art 48253 226154455 2008-07-17T01:50:55Z Seba5618 2155335 Reverted 2 edits by [[Special:Contributions/Fractalia|Fractalia]] identified as [[WP:VAND|vandalism]] to last revision by [[User:Prolog|Prolog]]. ([[WP:TW|TW]]) [[Image:InterstellarDoilies-1024.jpg|thumb|150px|right|A fractal image generated by Sterling Fractal by Stephen Ferguson.]] '''Fractal art''' is created by calculating [[fractal]] objects and representing the calculation results as still images, animations, [[Algorithmic composition|music]], or other media. Fractal art is usually created indirectly with the assistance of a [[computer]], iterating through three phases: setting parameters of appropriate fractal software, executing the possibly lengthy calculation and evaluating the product. Fractal objects fall into four main categories depending on how an artist can manipulate their construction and rendering to exercise artistic control over the resulting fractal art: * Escape time fractals that are manipulated with the choice of the formula to be iterated and its parameters, the choice of what points are iterated (usually a tiny region of the complex plane containing interesting shapes) and how they are mapped to an image, the choice of how to compute a colour from the set of sequences of iterations. All these components have an explicitly mathematical and nonvisual nature and they can often be very complex. Examples of this type of fractal are the [[Mandelbrot set|Mandelbrot]] and [[Julia set|Julia sets]], the [[Lyapunov fractal]], the [[Newton fractal]], its relative the [[Nova fractal]], and the [[Burning Ship fractal]]; some fractal image creation programs for this type of fractal art are [[Ultra Fractal]], [[Gnofract4D]], [[ChaosPro]] and [[Fractint]]. * [[Lindenmayer systems]] and other constructions based on replacement rules. Examples include the [[Peano curve]] and the [[Hilbert curve]], the [[Sierpinski gasket]] and the [[Menger sponge]], and the [[Koch snowflake]]. Stochastic systems where the replaced shapes and/or the choice of rules are random are very popular, especially to recreate trees and other natural objects. [[Image:Www_y23_com--fractal----Lg_Z010121Z.jpg|left|200px|thumb|Child's Play by Karl Scherer]] Design relies on simple geometry (angles and lengths) and being able to predict the shapes resulting from a rule system, and the possibility of fast or realtime previews of the result greatly facilitates small adjustements of sizes, angles and probabilities. * [[Iterated function system]]s and variants thereof ([[fractal flame]]s in particular); shapes and colours are determined by easily understood transformations of shrunk copies of the whole pattern, and since the transformation matrices and deformations have no particular significance they are usually input in fractal software visually and often with a realtime preview; another trend is manual editing starting from a random fractal (the arbitrary parameters are many and mostly independent). [[Apophysis (software)|Apophysis]] is a popular and very sophisticated example of this category. * [[Stochastic]] synthesis of [[fractal noise]] (typically [[fractal landscapes]]) controlled through few simple high level parameters and by trying different [[Pseudorandom number generator]] seeds. Fractals of all four kinds have been used as the basis for digital art and animation. 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. 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 like 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. == See also == * [[Systems art]] ==Further reading== *{{cite book|first=John|last=Briggs|title=Fractals|isbn=0-671-74217-5}} *{{cite book|first=Clifford|last=Pickover|authorlink=Clifford A. Pickover|title=Computers, Pattern, Chaos and Beauty|isbn=0-486-41709-3}} *{{cite book|first=Manfred|last=Schroeder|Fractals, Chaos, Power Laws|isbn=0-7167-2357-3}} *Michael Michelitsch and Otto E. Rössler, The "Burning Ship" and Its Quasi-Julia Sets, Computers & Graphics Vol. 16, No. 4, pp. 435-438, 1992, reprinted in [9] *Michael Michelitsch and Otto E. Rössler, "A New Feature in Hénon's Map." Comput. & Graphics Vol. 13, No. 2, pp. 263-265, 1989, reprinted in [9] ==External links== * {{dmoz|Science/Math/Chaos_and_Fractals/Fractal_art/|Fractal Art}} * [http://commons.wikimedia.org/wiki/Mandelbrot_set#Some_details_of_the_Mandelbrot_set Art and the Mandelbrot set (in commons.wikimedia)] [[Category:Fractals]] [[Category:Computer art]] [[Category:Digital art]] [[de:Fraktalkunst]] [[fr:Art fractal]] [[gl:Arte fractal]] [[it:Arte frattale]] [[ja:フラクタルアート]] [[pt:Arte fractal]] [[sv:Fraktalkonst]]