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:
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 which are generated by stochastic rather than deterministic processes (examples include fractal landscapes).
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.
External Links
- Ultra Fractal - software for creating Fractal Art:
- The Infinite Fractal Loop - a web ring of Fractal Art
- XAOS - an open source fractal generator
- Soler's Fractal site
- Mathsong Fractal Art