< 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)