fractal

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Related to Fractal curve: fractal dimensionality

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 ?
A novel circularly arched fractus named Arched Bow-shaped Fractal Curve (ABFC) is originally proposed.
And the Koch fractal curve appeared in 1904 after a publication of the mathematician Niels Fabian Helge von Koch [14,15].
1991], and fractal curve generation [Ohno and Ohyama 1991; Peitgen et al.
In this paper, we propose a novel circularly arced Koch fractal curve (CAKC).
The arm length was repeatedly subdivided to obtain fractals upto three iterations using the concept of the Koch fractal curve.