fractal

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Related to Fractal curve: fractal dimensionality

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 ?
In this study, the aggregate particles' fractal dimension was measured by the slit island method, which calculates the fractal dimension, D, by utilizing the perimeter, P, and the surrounding region's area, A, of the enclosed fractal curve, C.
D fractal dimension (FD) is called a fractal curve.
One such fractal curve is Hilbert Curve, first introduced by David Hilbert.
In this paper, we originally propose a novel circularly arched bow-shaped fractal curve and construct a loop with four such fractal curves cascaded end-to-end.
To reject insertion loss and heighten selectivity, left handed materials (LHMs) and fractal curve have been widely used in the design of coupled resonator filters [4-7] in recent years.

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