A fractal is a special image that is often generated using very simple mathematical rules. If you take a smaller portion of the image and then magnify it, you find a new image within, which is just as complicated. The image can be magnified millions of times, and in each case, a new image is revealed. Many fractals are very interesting to look at, and the rules are very important in the field of computer generated graphics, as they allow very complicated objects to be created quickly.
For information on fractals, please visit the Wikipedia article.