fractal

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Related to Fractals: Mandelbrot set, Mandelbrot

frac·tal

(frăk′təl)
n.
An object whose parts, at infinitely many levels of magnification, appear geometrically similar to the whole. Fractals are used in the design of compact antennas and for computer modeling of natural-looking structures like clouds and trees.

[French, from Latin frāctus, past participle of frangere, to break; see fraction.]

fractal

(ˈfræktəl) maths
n
(Mathematics) a figure or surface generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process
(Mathematics) of, relating to, or involving such a process: fractal geometry; fractal curve.
[C20: from Latin frāctus past participle of frangere to break]

frac•tal

(ˈfræk tl)

n.
a geometrical structure that has a regular or an uneven shape repeated over all scales of measurement and that has a dimension (frac′tal dimen`sion), determined according to definite rules, that is greater than the spatial dimension of the structure.
[< French fractale < Latin frāct(us) broken, uneven; term introduced by French mathematician Benoit Mandelbrot (born 1924) in 1975]

frac·tal

(frăk′təl)
A geometric pattern repeated at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by standard geometry. Even the most minute details of a fractal's pattern repeat elements of the overall geometric pattern. Fractals are widely used in computer modeling of irregular patterns and structures in nature, such as the patterns of seasonal weather. They are also considered to be a visual representation of chaos. See more at chaos.
ThesaurusAntonymsRelated WordsSynonymsLegend:
 Noun 1 fractal - (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometrypattern, form, shape - a perceptual structure; "the composition presents problems for students of musical form"; "a visual pattern must include not only objects but the spaces between them"math, mathematics, maths - a science (or group of related sciences) dealing with the logic of quantity and shape and arrangement
Translations
fractalfractale

fractal

[ˈfræktəl] (Geom)
B. N
C. CPD fractal geometry N

fractal

[ˈfræktəl] n
References in periodicals archive ?
Furthermore, since its Mandelbrot's discover, fractals are becoming a powerful new mathematical language, thanks to which it is possible to describe natural phenomena and solve the real natural problems that had once been set aside.
The Mandelbrot's set (figure no.2) is one of the most popular fractals, also known outside the mathematical field due to the suggestive multicolored images that have been disclosed.
Touching on pancake fractals, crop circles, and art from around the world, this color-illustrated introduction for general readers and students celebrates the life, work, and legacy of Benoit Mandelbrot, the visionary mathematician who refined and promoted work on fractal geometry.
Clouds are Not Spheres: A Portrait of Benoit Mandelbrot the Founding Father of Fractal Geometry
Bijaksana, "3D fractal dimension and flow properties in the pore structure of geological rocks," Fractals.
Hu, "Recent advances on fractal modeling of permeability for fibrous porous media," Fractals, vol.
Jiang, "Fractal characteristics of crack propagation in coal under impact loading," Fractals, vol.
The results above allow one to obtain the Callan-Symanzik equation for the fractals considered here; that is,
Measuring the dimension of self-affine fractals: example of rough surfaces, Chapter 4 in C.
A very interesting and very popular approach to represent rough surfaces encountered in real--life has been proposed by Mandelbrot and other scientists, who presented the concept of fractals , .
The new patented and patent pending technology utilizes a discovery made over a dozen years ago during the research on invisibility cloaks, themselves invented first (see US patent 8,253,639) and patented by FRACTAL. While reducing the reflected "scattering" to a radar signal, FRACTAL not only found a way to make the reflections disappear, but also found other unique fractal-based solutions that actually enhanced radar reflection.
 studied the microstructure features of FeCrAl fiber materials and obtained the fractal dimensions by the scanning electron microscope (SEM) photographs.

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