A fractal is a geometric object that retains its complexity under any level of magnification. Many fractals are self-similar in that the fractal image is infinitely repeated on a smaller scale as one "zooms" into the object. The most famous of the fractal objects is the Mandelbrot Set named after its discoverer, Benoit B. Mandelbrot. As you can see in the accompanying images, the Mandelbrot Set, a bug-shaped object, appears again and again as one magnifies the image.
Fractals are not simply an abstract geometric concept. Fractals appear everywhere in nature: from the irregular shape of a coastline to the outlines of trees, clouds, and mountains. The application of fractal geometry to science and physics has allowed mathematicians and physicists to describe phenomena that had, until recently, eluded description.
Fractals have also been used in image processing. Mathematician Michael F. Barnsley has applied fractal mathematics to the compression of digital photographs and video images. Because of their beauty, fractals are a popular source of computer art as well.