fractal

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fractal

[′frakt·əl]
(mathematics)
A geometrical shape whose structure is such that magnification by a given factor reproduces the original object.

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". 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].

References in periodicals archive ?
The system uses the advantages of fractal geometry, in particular the wide range of fractal sets and the speed of its generation.
Montrucchio and Privileggi (1999) borrowed from the literature on fractal images generation (specifically, from the 'Collage Theorem' by Hutchinson, 1981; Barnsley, 1989; Vrscay, 1991) to show that standard stochastic concave optimal growth models may exhibit optimal trajectories which are random processes converging to singular invariant distributions supported on fractal sets regardless of the discount factor.
This correspondence can be used in order to define a Laplacian on fractal sets which are often used to model 'wild', 'irregular', and 'rough' things.