Fractal art

Fractal art is an algorithmic approach for producing Computer-generated art using fractal mathematics. Traditionally, fractals fall into three 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. 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 which are generated by stochastic rather than deterministic processes (examples include fractal landscapes).

Fractals of all three 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.

Many fractal art galleries can now be found on the Internet. Perhaps a good starting point would be the fractal pages of Stephen C. Ferguson who has made several fractal generators--for example http://www.eclectasy.com/Iterations-et-Flarium24. 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. For an example of a fractal viewer see http://www.efractal.com.