The illustrations accompanying this article are designs derived from a mathematical discipline that produces images called "fractals." This word was coined by the French theorist Benoit Mandelbrot in 1975, and was used to describe the bizarre configurations that emerged from his unique mathematical analysis of the physical world. In that year, he revolutionized the way that science looks at a landscape. Two years later, he published the landmark Fractals: Form, Chance and Dimension.
What is a fractal? The Oxford American Dictionary calls it "… a curve or geometric figure, each part of which has the same character as the whole. Fractals are useful in modeling structures (such as eroded coastlines or snowflakes) in which similar patterns recur at progressively smaller scales, and in describing partly random or chaotic phenomena such as crystal growth, fluid turbulence, and galaxy formation."
The word itself is derived from French, and the Latin fract, meaning "broken."
Observe that in the above definition, everything from crystals to galaxies can be described by fractal geometry. Large structures can be broken down into smaller and smaller ones, ad infinitum. Likewise, small structures can be expanded into larger ones … into infinity.