Definitions for

**"Fractal geometry"**Submitted By The Authors While the classical Euclidean geometry deals only with objects which exist in integer dimensions, fractal geometry works with objects in non-integer dimensions, known as fractal dimensions. While Euclidean geometry is a description of lines, ellipses, circles, etc, fractal geometry is described in algorithims, or a set of instructions on how to create a fractal. More information is available at the fractal geometry main page.

the geometry of fractals; "Benoit Mandelbrot pioneered fractal geometry"

A nascent branch of mathematics named with a Latin word meaning irregular. Fractal geometry explores a world of crinkly convoluted shapes far removed from the straight lines and smooth curves of traditional Euclidean geometry. Fractal curves, produced by computer algorithms, bear striking resemblance to naturally occurring shapes (coastlines, clouds, etc.) and hence are extensively used to produce realistic computer graphics. The term "fractal" is also an abbreviation for "fractional dimension": the dimensions of fractal curves are not limited to integers. These curves are used to model chaotic phenomena appearing in such diverse fields as music, financial markets, and natural topology.