fractal

n. groups that have broken dimensions so that each one looks like an exact copy of the second (like the Mandelbrot group in Mathematics); (In Computers) geometric shapes that have interesting contour lines

A fractal is generally "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a reduced-size copy of the whole," a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured".
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Noun
1. (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry
(hypernym) form, shape, pattern
(classification) mathematics, math, maths

n. fractal, groups that have broken dimensions so that each one looks like an exact copy of the second (like the Mandelbrot group in Mathematics); (In Computers) geometric shapes that have interesting contour lines

<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". He defines a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals.
sci.fractals FAQ.
See also fractal compression, fractal dimension, Iterated Function System.
Usenet newsgroups: news:sci.fractals, news:alt.binaries.pictures.fractals, news:comp.graphics.
["The Fractal Geometry of Nature", Benoit Mandelbrot].
[Are there non-self-similar fractals?]
(1997-07-02)