Fractal art is created by calculating fractal objects and representing the calculation results as still images, animations, music, or other media. A fractal is generally "a rough or fragmented geometric shape that can be split into parts each of which is (at least approximately a reduced-size copy of the whole" Algorithmic composition is the technique of using algorithms to create Music. 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. A computer is a Machine that manipulates data according to a list of instructions.
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 and 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. In Mathematics, the Mandelbrot set, named after Benoît In Complex dynamics, the Julia set J(f\ of a Holomorphic function f\ informally consists of those points whose long-time behavior under In Mathematics, Lyapunov fractals (also known as Markus-Lyapunov fractals) are bifurcational Fractals derived from an extension of the The Newton fractal is a boundary set in the Complex plane which is characterized by Newton's method applied to a fixed Polynomial p(Z\in\mathbb{C} Nova fractal refers to a family of fractals related to the newton fractal. The Burning Ship fractal, first described and created by Michael Michelitsch and Otto E Ultra Fractal is a Fractal generation and rendering software application. Fractint is a Freeware software package that can render and display many kinds of Fractals Its name comes from the words fractal and Integer
- Lindenmayer systems and other constructions based on replacement rules. An L-system or Lindenmayer system is a parallel rewriting system, namely a variant of a Formal grammar (a set of rules and symbols most famously used Examples include the Peano curve and the Hilbert curve, the Sierpinski gasket and the Menger sponge, and the Koch snowflake. Space-filling curves or Peano curves are Curves first described by Giuseppe Peano (1858–1932 whose ranges contain the entire 2-dimensional Unit A Hilbert curve (also known as a Hilbert space-filling curve) is a continuous Fractal Space-filling curve first described by the German mathematician The Sierpiński triangle, also called the Sierpiński gasket or the Sierpiński Sieve, is a Fractal named after Wacław Sierpiński who described In Mathematics, the Menger sponge is a Fractal curve It is the universal curve, in that it has Topological dimension one and any other The Koch snowflake (or Koch star) is a mathematical Curve and one of the earliest Fractal curves to have been described 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.
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 systems and variants thereof (fractal flames 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). In Mathematics, iterated function systems or IFS s are a method of constructing Fractals the resulting constructions are always Self-similar. Fractal flames are a member of the Iterated function system class of Fractals created by Scott Draves in 1992 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. Stochastic (from the Greek "Στόχος" for "aim" or "guess" means Random. A fractal landscape is a surface generated using a Stochastic algorithm designed to produce Fractal behaviour which mimics the appearance of natural terrain A pseudorandom number generator ( PRNG) is an Algorithm for generating a sequence of numbers that approximates the properties of random numbers
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 flames 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. In Artificial intelligence, an evolutionary algorithm (EA is a Subset of Evolutionary computation, a generic population-based Metaheuristic Electric Sheep is a Distributed computing project for animating and evolving Fractal flames which are in turn distributed to the networked computers which display Fractal flames are a member of the Iterated function system class of Fractals created by Scott Draves in 1992 Distributed computing deals with Hardware and Software Systems containing more than one processing element or Storage element concurrent A screensaver is a type of computer program initially designed to prevent " Phosphor burn-in " on CRT and plasma Computer
See also
Further reading
- Briggs, John. Systems art is Art influenced by Systems theory, which reflects on natural systems social systems and social signs of the Art world itself Fractals. ISBN 0-671-74217-5.
- Pickover, Clifford. Clifford A Pickover is an American author editor and columnist in the fields of Science, Mathematics, and Science fiction, and is employed at the Computers, Pattern, Chaos and Beauty. ISBN 0-486-41709-3.
- Schroeder, Manfred. {{{title}}}. 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
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