FROM THE WEBSITE "SCIENCE CLARIFIED": "A fractal is a geometric figure with two special properties. First, it is irregular, fractured, fragmented, or loosely connected in appearance. Second, it is self-similar; that is, the figure looks much the same no matter how far away or how close up it is viewed. The term fractal was invented by Polish French mathematician Benoit Mandelbrot (1924– 2010) in 1975. He took the word from the Latin word fractus, which means "broken." The idea behind fractals is fairly simple and obvious when explained. But the mathematics used to develop those ideas is not so simple. Most objects in nature do not have simple geometric shapes. Clouds, trees, and mountains, for example, usually do not look like circles, triangles, or pyramids. Instead, they can best be described as fractals. Fractals are used by geologists to model the meandering paths of rivers and the rock formations of mountains; by botanists to model the branching patterns of trees and shrubs; by astronomers to model the distribution of mass in the universe; by physiologists to model the human circulatory system; by physicists and engineers to model turbulence in fluids; by economists to model the stock market and world economics." [CHP editor's note: And by movie special effects and CGI specialists to create natural-looking artificial landscapes, and artists like Janet Parke (see image above) to produce gorgeous abstract images.]

Michael Frame, Benoit Mandelbrot, and Nial Neger, Fractal Geometry (Yale University, December 3, 2004)

Truly amazing. This is an on-line collection of pages meant to support a first course in fractal geometry for students without especially strong mathematical preparation, or any particular interest in science. In includes a vast array of practical explanations and other resources, working Java applications, etc., covering a vast array of applications of fractal theory.

https://users.math.yale.edu/public_html/People/frame/Fractals/

Internet Resources for Fractals (an extensive web bibliography with links)

http://math.fullerton.edu/mathews/c2003/FractalBib/Links/FractalBib_lnk_1.html

What is a fractal?

http://www.laubender.de/fractaline/what_is_a_fractal.htm

The Fractal Geometry of the Mandelbrot Set

http://math.bu.edu/DYSYS/FRACGEOM/FRACGEOM.html

A Mandelbrot set animation from http://members.rogers.com/ender.othc/images/mandelzoom.mpeg