A word coined by mathematician Benoit Mandelbrot in 1975 to describe a class of shapes characterized by irregularity, but in a way that evokes a pattern. Computer graphics technicians often use fractals to generate naturelike images such as landscapes, clouds, and forests. The distinguishing characteristic of fractals is that they are “self-similar”; any piece of a fractal, when magnified, has the same character as the whole. The standard analogy is that of a coastline, which has a similar structure whether viewed on a local or continental scale. Interestingly, it is often difficult to measure the length of the perimeter of such a shape exactly because the total distance measured depends on the size of the smallest element measured. For example, one could measure on a given coastline the perimeter of every peninsula and inlet, or at a higher magnification the perimeter of every small promontory and jetty, and so on. In fact, a given fractal may have a finite area but an infinite perimeter; such shapes are considered to have a fractional dimension—for example, between 1 (a line) and 2 (a plane)—hence the name fractal. See the illustration. See also cellular automata, graftal.
A geometric pattern that is repeated at every scale and so cannot be represented by classical geometry.
Irregular shape or surface produced by a procedure of repeated subdivision. Generated on a computer screen, fractals are used in creating models for geographical or biological processes (for example, the creation of a coastline by erosion or accretion, or the growth of plants).
Sets of curves with such discordant properties were developed in Germany by Georg Cantor (1845–1918) and Karl Weierstrass (1815–1897). The name was coined by the French mathematician Benoit Mandelbrod. Fractals are also used for computer art.
Fractal compression is a method of storing digitally processed picture images as fractals. It uses less than a quarter of the data produced by breaking down images into pixels. The technique was first used commercially in CD-ROM products 1993.