# 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]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## 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
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
Translations
fractalfractale

## fractal

[ˈfræktəl] (Geom)
B. N
C. CPD fractal geometry N
Collins Spanish Dictionary - Complete and Unabridged 8th Edition 2005 © William Collins Sons & Co. Ltd. 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005

## fractal

[ˈfræktəl] n
Collins English/French Electronic Resource. © HarperCollins Publishers 2005
References in periodicals archive ?
1, it can get a fractal curve. It is the attractor G of IFS{[R.sup.2]: [W.sub.1],[W.sub.2],...,[W.sub.N]}
When the fractal figure covers the fractal curve image with a square lattice of a certain scale, some of the mesh may contain part of the curve, while other parts of the mesh remain empty, with the number of nonempty mesh increasing as the mesh side length gradually reduces.
In , a novel Koch-like fractal curve is proposed to transform an ultrawideband (UWB) bow-tie into a so-called Koch-like sided fractal bow-tie dipole.
D fractal dimension (FD) is called a fractal curve. FD diagram sharp peaks indicate a structural defect is the place.
Next, we will see that Hausdorff measure indeed determines the dimension of a fractal curve but does not describe its analytic properties, for example, the self-similarity between local and global shapes of 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.
After the first iteration, the 1st-iteration tree fractal curve is obtained, called "T1".
Contrary to Euclidean geometrical objects, the fractal dimension of a fractal curve is not an integer.

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