Fractal art
From Wikipedia, the free encyclopedia
Fractal art is created by calculating fractal mathematical functions and transforming the calculation results into still images, animations, music, or other art media. Fractal images are graphs of the calculation results, and fractal animations are sequences of these graphs. Fractal music maps the calculation results to music pitches or other sounds. Fractal art is usually created with the assistance of a computer, in order to speed up the process of calculating the fractal function.
Fractals fall into four broad categories relevant to fractal art:
- Those for which membership of a point in a fractal set may be determined by iterative application of a simple function. Examples of this type are the Mandelbrot set, the Lyapunov fractal, and the Burning Ship fractal.
- Those for which a geometric replacement rule exists. Examples include Cantor dust, the Sierpinski gasket, the Menger sponge and the Koch snowflake.
- Those created with iterated function systems, in particular fractal flames.
- Those which are generated by stochastic rather than deterministic processes (examples include fractal landscapes).
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 also being used in context with evolutionary algorithms in the Electric Sheep project, as people use fractals rendered with distributed computing as their screensaver, and "rate" the flame they are viewing. Then the server reduces the traits of the undesirables, and increases those of the desirables to produce a computer-generated, community-created piece of art.
The two most popular fractal image creation programs are probably Ultra Fractal and Apophysis. The latter is a fractal flame editor and the former a more general purpose fractal program. During the 1990s Fractint for DOS was the most popular fractal rendering software for the PC.
Fractal music is able to produce more realistic natural sounds and subtle tunes than conventional approaches.
[edit] References
- [1] John Briggs, Fractals ISBN 0-671-74217-5
- [2] Clifford A. Pickover, Computers, Pattern, Chaos and Beauty ISBN 0-486-41709-3
- [3] Clifford A. Pickover, Fractal Horizons, ISBN 0-312-12599-2
- [4] Clifford A. Pickover, Chaos and Fractals ISBN 0-444-50002-2
- [5] Clifford A. Pickover, Keys to Infinity ISBN 0-471-19334-8
- [6] Manfred Schroeder, Fractals, Chaos, Power Laws ISBN 0-7167-2357-3
- [7] 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]
- [8] 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]
- [9] Clifford A. Pickover Ed., Chaos and Fractals: A Computer Graphical Journey - A 10 Year Compilation of Advanced Research. Amsterdam, Netherlands: Elsevier 1998. ISBN 0-444-50002-2
[edit] External links
- Apophysis – Open Source fractal flame editor for Windows
- The Fractal Art Manifesto – essay by Kerry Mitchell
- Ultra Fractal – non-free software for creating fractal images and animations
- The Infinite Fractal Loop – a web ring of Fractal Art
- XaoS – open source software for creating fractal images and animation
- The Electric Sheep a distributed computing project to render animated fractal flames.
- Art and the Mandelbrot set (in commons.wikimedia)
