Fractals are mathematical functions of complex variables.
Fractals can model phenomena of nature such as spiral galaxies, ferns, and sea-horses, but fractals also offer tremendous geometrical complexity and colour variation far removed from the ordinary. Also, fractal images are often symetrical about an axis. Total chaos is thus avoidable and it is possible to achieve enough subtlety of pattern to sustain interest. The immaculate precision of the rendering can be compelling and, in a way, challenging to the viewer. I think that for artists, fractals are a medium, like paint.