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Related to fractal: Fractal dimension


A geometrical shape whose structure is such that magnification by a given factor reproduces the original object.


(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].

References in periodicals archive ?
Geometrically, the art-like fractals act as the tiny resonators envisioned by Huygens to make the ensemble of wavelets.
2] > 1) are the spatial-frequency scaling parameters, b is a constant (b > 1), D (2 < D < 3) is the roughness fractal dimension, [K.
Mandelbrot's most famous and influential work was his 1985 book titled The Fractal Geometry of Nature (Gomory, 2010).
And as for Wilwayco, he is fully aware that, whether the series continues or not, his fractal attraction will always be there to color his existence.
He stated that fractals (through fractal geometry) are more useful to describe natural shapes than the classic Euclidian geometry describes.
The previous constructions allow us the definition of fractal bases of the space of square-integrable functions on I .
To illustrate how fractal dimension based algorithm works, we chose one mammography case which contains architectural distortion.
RESULT: In Group I fractal dimensions were ranging from 1.
The novel approach of embedding first order Koch fractal geometry in the pentagonal patch antenna is used for achieving miniaturization in the overall size of the pentagon patch.
One of the most interesting techniques to create metallic structures with random fractal shapes is electrochemical deposition.
In fact, fractal structures in ecological ecosystems such as coral reefs have been recognized by researchers since the 1980s (BRADBURY; REICHELT, 1983).