Fractals are complex geometric patterns that sometimes resemble natural objects. Although mathematicians have been aware of some fractal patterns since the 19th century, Polish-born mathematician Benoit Mandelbrot (pronounced ben-WAH MAN-dul-bro) is credited with putting the study of fractals on a systematic footing in the late 1970s. Mandelbrot invented the word "fractal" and argued that by using fractals scientists should be able to describe many natural processes that had previously been too unruly for the neat formulae of traditional mathematics (even those of probability and statistics). As it turned out, he was right. Fractals have also proved useful in the field of computer graphics.

"Fractal" comes from the Latin word fractus, meaning "broken"; fractal patterns are not composed of smooth lines, but are infinitely broken up. (Technically, they are said to be "nondifferentiable.") The closer one looks at an ideal fractal, the more detailed structure one sees...