For those mathematically inclined, a fractal is a graphic representation of a whole bunch of complex numbers. The numbers are plotted on a plane with the real-number component representing the distance left or right of the center, and the imaginary component representing the distance above or below the center.
For the rest of us, a fractal is just cool eye candy.
There are several types of fractals, the most famous being the Mandelbrot set. In Fractal eXtreme, several other types are available for you to explore.
Fractals appear in fractal windows.