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. Sierpinskitriangle, 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, IteratedFunction 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)