Fractal art - Definition

Fractal art is an algorithmic approach for producing computer-generated art using fractal mathematics. Traditionally, fractals fall into four broad categories relevant to fractal art:

Computer-generated fractal image.

• Those for which membership of a point in a fractal set may be determined by iterative application of a simple function. An example of this type is the Mandelbrot set and the Lyapunov 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 vast sections of 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.

For an example of the state of the art in fractal landscapes, http://www.fractal-landscapes.com contains an excellent gallery and a description of the mathematics behind fractal landscapes.

Additionally, a sub-category of fractal art is fractal music which is able to produce more realistic natural sounds and subtle tunes than conventional approaches.

References

• John Briggs, Fractals ISBN 0671742175
• Clifford A. Pickover, Computers, Pattern, Chaos and Beauty ISBN 0486417093
• Clifford A. Pickover, Fractal Horizons, ISBN 0312125992
• Clifford A. Pickover, Chaos and Fractals ISBN 0444500022
• Clifford A. Pickover, Keys to Infinity ISBN 0471193348
• Manfred Schroeder, Fractals, Chaos, Power Laws ISBN 0716723573

External links

• The Fractal Art Manifesto (http://www.fractalus.com/info/manifesto.htm) – What fractal art is and is not
• Of Fractals and Art (http://www.fractalus.com/info/fractalart.htm)
• Yahoo group for exploring the Mandelbrot set (http://groups.yahoo.com/group/mandelbrotexplorers/join)
• Ultra Fractal (http://www.ultrafractal.com) – software for creating Fractal Art
• C82 (http://www.c82.net) – Inspirational fractal art grallery geared towards redefining fractal art
• The Infinite Fractal Loop (http://www.fractalus.com/ifl/) – a web ring of Fractal Art
• XAOS (http://xaos.sourceforge.net/) – an open source fractal generator
• Mathsong Fractal Art (http://www.mathsong.com/fractal/)
• Fractal Flames (http://flam3.com/)
• Phidelity Fractal Art (http://www.phidelity.com/ph2/fractals/) – Fractal Art Gallery and Spot Files for Fractal Explorer
• Fractal Recursions (http://www.fractal-recursions.com/)
• The Electric Sheep (http://www.electricsheep.org/) Project – a distributed computing project to render animated fractal flames.
• Ultra Fractal parameters database (http://www.ufdbparam.info/)