Friday, November 14, 2008

Definitions of a Fractal

For those of you who don't know:-

noun Mathematics, Physics.
a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

[Origin: < F fractale, equiv. to L frāct(us) broken, uneven (see fractus) + -ale -al2; term introduced by French mathematician Benoit Mandelbrot (born 1924) in 1975]

[1] fractal. (n.d.). Unabridged (v 1.1). Retrieved November 18, 2008, from website: [link]

FRACTAL-n. A geometric pattern that is repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Fractals are used especially in computer modeling of irregular patterns and structures in nature.

[French, from Latin frāctus, past participle of frangere, to break; see fraction.]

The American Heritage® Dictionary of the English Language, Fourth Edition
Copyright © 2006 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.

FRACTAL- mathematics, graphics
A fractal is a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller copy of the whole. Fractals are generally self-similar (bits look like the whole) and independent of scale (they look similar, no matter how close you zoom in).

Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines.
Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break".

The Free On-line Dictionary of Computing, © 1993-2007 Denis Howe

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