fractal


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Related to fractal: Fractal dimension

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 ?
Because of these considerations, we decided to seek for multidimensional fractal characteristics that would be free of the presumption of self-similarity and applicable in the fractography of fatigue fractures.
Fractals exist in mountains, trees, snowflakes, flowers, clouds, and even the random scattering of leaves on the pavement.
Rather than just nature's leftover imprint on our brains, fractal patterns are being found in things such as our heart rhythm and eye movements.
Computer models that simulate particles of rock trapped in a moving fault, as well as laboratory tests with pellets of crushed granite, also generate a distribution of particle sizes with a fractal dimension of 1.
Fractal techniques were developed because most spatial patterns of nature, such as curves and surfaces, are so irregular and fragmented that classical (Euclidean) geometry fails to provide tools for the analysis of their forms.
Fractal Variability versus Pathologic Periodicity: Complexity Loss and Stereotype in Disease.
6] that the reinforcement of carbon black loaded compound under high strain deformation can be explained by momentum transfers throughout fractal interfaces.
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Founded in 2000, Fractal provides advanced analytics to more than 50 Fortune 1,000 global companies.
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Fractal models in exploration geophysics; applications to hydrocarbon reservoirs.