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A geometrical shape whose structure is such that magnification by a given factor reproduces the original object.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.


(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,,

["The Fractal Geometry of Nature", Benoit Mandelbrot].

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The algorithm here uses a wide range of the fractal sets and the speed of its generation.
As solution survives a logarithmically fractal set (1) of transcendental frequency ratios.
In fractal geometry, the fractal dimension is the objective tool used to measure the degree of "irregularity" and "complexity" in two fractal sets. The fractal dimension definition has the following relations [33]:
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There are several methods available to estimate the dimension of fractal sets. The Hausdorff dimension is the principal definition of fractal dimension.
The studies of IFSs have provided powerful tools for the investigation of fractal sets that are used for approximation of natural or scientific data.