# 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.]

## 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 ?
For more than two decades, FRACTAL has explored, developed, and invented fractal-based electromagnetic technology, and used close-packed fractal resonators/fractal antennas for electromagnetic waves, with a broad and or multiband advantage.
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.
Here, an incident EM plane wave illuminates a three dimensional (3D) rough fractal surface f(x,y), where the illuminated area of the surface (due to limited radar antenna beamwidth) is given by A = 4[L.
Fractal dimension mapping us to ascertain geomorphic domains where variability of fractal dimension of the earth surface represents the roughness of the land form topography and is an assessment of texture of topography.
The fractal gel obtained from an aqueous dispersion of the first and second fractal particles, wherein the aqueous dispersion has a given pH; the first fractal particle has a surface charge at said given pH; and the second fractal particle has a surface charge of opposite polarity at said given pH.
A fractal has formally been defined as "a rough or fragmented geometric shape that can be subdivided in parts, each of which is (at least approximately) a smaller version of the whole" (Thomas, 2002, p.
What Wilwayco has done to this substrate is to engage it in a skirmish of his own volition, setting up a tension by asserting his own fractal trademarks in the form of repeated furrowed lines, effected from the combing of a top layer to reveal the multiplicity of colors and designs underneath.
In this paper, the author will experiment the use of an image processing technique, computing the fractal "box-counting" dimension of the time series corresponding to an asset price.
Since the advent of the fractal theory (and its predecessors) the emphasis has been on continuous functions (from Weierstrass map to wavelets) being the discontinuous case minimal.
In mammography, normal breast parenchyma behaves as a fractal object.
PISRS International Conference on Analysis, Fractal Geometry, Dynamical Systems and Economics (2011: Sicily, Italy).
AIM: The aim of this study was to use fractal geometry to compare the morphometric complexity in the normal andsquamous cell carcinoma of the buccal mucosa, which was fulfilled by estimating the fractal dimensions of ECTI profiles, isolated from histological sections of the tissue specimens.

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