fractal


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Related to fractal: Fractal dimension

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.]

frac′tal adj.

fractal

(ˈfræktəl) maths
n
(Mathematics) a figure or surface generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process
adj
(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:
Noun1.fractal - (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry
pattern, 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)
A. ADJfractal
B. Nfractal m
C. CPD fractal geometry Ngeometría f fractal

fractal

[ˈfræktəl] nfractale f
References in periodicals archive ?
The financier Bill Williams has developed the fractal indicator it and can be used in all markets and in all time periods [5].
FRACTAL has dubbed the new system for tracking and identification as "RDiD(TM)".
Since Mandelbrot first proposed the fractal theory in 1980s [3], its application has been widely used for rock pore structure characterization, due to its effectiveness in describing complex and irregular structures with self-similar characteristics.
In this paper, damage variables are redefined by AE parameters, the number of cycles, and the fractal dimension, and the expression of damage variable is corrected.
Fractal tree microstrip antenna is covered with the NaCl.
This system can be shown to have a fractal dimension in the energy-momentum space, so from now on it will be referred to as fractal.
For example, Zhang [5] proposed a fractal model for normal contact stiffness of machine joint surfaces based on Hertz contact theory between a sphere and a plane under some given hypotheses.
The first goal of this study is to measure the sprawl and complexity of the adjacent administrative districts of Atakum, Ilkadim and Canik in Samsun, Turkey in the years 1989, 2000 and 2013, during which these districts experienced rapid growth, using Shannon's entropy and fractal analysis based on remote sensing and GIS.
4i will operate as a wholly owned subsidiary of Fractal Analytics and will continue delivering services to clients, while getting immediate access to Fractal Analytics' IP, capabilities, infrastructure and talent.
Regarding the modeling of the 3D rough fractal surface, we introduce here a bandlimited Weierstrass function of two variables, (1) below, as a straightforward extension of similar Weierstrass functions provided in the past by Jaggard [8] (function of one variable) and by Zaleski [10] (function of two variables).
Fractal techniques have been used in diverse engineering applications involving physical phenomenon in disordered structures and multiple scales [22,23].