What is a fractal? Here's a definition:
Mathematician Benoit Mandelbrot's term for shapes that are "self-similar," appearing the same at different magnifications. A fractal can be created by duplicating a shape successively according to a set of rules. The results can be complex structures, which resemble seemly random-shaped things in nature, such as clouds, trees, and mountains. An application of fractals is to represent complex imagery in very concise algorithms.
Does that help at all? I didn't think so. Basically, take a mathematical formula, have your computer crank through the different X and Y variables, and you get a cool picture. Then zoom in on a section of the image, and you get the cool picture again! And with even more detail. Then zoom in again. And again.
The fractals on Fractal of the Day were generated with Fracture, from Stick Software.
These images were created by Michael Clark, but you may use them as you wish long as you provide a clickable link to FractalOfTheDay.com (if you use an image on a web site), or if in print or offline, print the FractalOfTheDay.com URL somewhere.