noun Mathematics, Physics.
a geometrical or physical structure having an irregular or fragmented shape at all scales of measurement between a greatest and smallest scale such that certain mathematical or physical properties of the structure, as the perimeter of a curve or the flow rate in a porous medium, behave as if the dimensions of the structure (fractal dimensions) are greater than the spatial dimensions.

< French fractale, equivalent to Latin frāct(us) broken, uneven (see fractus) + -ale -al2; term introduced by French mathematician Benoit Mandelbrot (born 1924) in 1975 Unabridged
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World English Dictionary
fractal (ˈfræktəl)
1.  a figure or surface generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative process
2.  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 & Unabridged 10th Edition
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Word Origin & History

1975, from Fr., from L. fractus "broken," pp. of frangere "to break" (see fraction). Coined by Fr. mathematician Benoit Mandelbrot in "Les Objets Fractals."
Online Etymology Dictionary, © 2010 Douglas Harper
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American Heritage
Science Dictionary
fractal   (frāk'təl)  Pronunciation Key 

(click for larger image in new window)

A complex geometric pattern exhibiting self-similarity in that small details of its structure viewed at any scale repeat elements of the overall pattern. See more at chaos.

Our Living Language  : Fractals are often associated with recursive operations on shapes or sets of numbers, in which the result of the operation is used as the input to the same operation, repeating the process indefinitely. The operations themselves are usually very simple, but the resulting shapes or sets are often dramatic and complex, with interesting properties. For example, a fractal set called a Cantor dust can be constructed beginning with a line segment by removing its middle third and repeating the process on the remaining line segments. If this process is repeated indefinitely, only a "dust" of points remains. This set of points has zero length, even though there is an infinite number of points in the set. The Sierpinski triangle (or Sierpinski gasket) is another example of such a recursive construction procedure involving triangles (see the illustration). Both of these sets have subparts that are exactly the same shape as the entire set, a property known as self-similarity. Under certain definitions of dimension, fractals are considered to have non-integer dimension: for example, the dimension of the Sierpinski triangle is generally taken to be around 1.585, higher than a one-dimensional line, but lower than a two-dimensional surface. Perhaps the most famous fractal is the Mandelbrot set, which is the set of complex numbers C for which a certain very simple function, Z2 + C, iterated on its own output (starting with zero), eventually converges on one or more constant values. Fractals arise in connection with nonlinear and chaotic systems, and are widely used in computer modeling of regular and irregular patterns and structures in nature, such as the growth of plants and the statistical patterns of seasonal weather.
The American Heritage® Science Dictionary
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American Heritage
Cultural Dictionary
fractal [(frak-tuhl)]

Contraction of “fractional dimension.” This is a term used by mathematicians to describe certain geometrical structures whose shape appears to be the same regardless of the level of magnification used to view them. A standard example is a seacoast, which looks roughly the same whether viewed from a satellite or an airplane, on foot, or under a magnifying glass. Many natural shapes approximate fractals, and they are widely used to produce images in television and movies.

The American Heritage® New Dictionary of Cultural Literacy, Third Edition
Copyright © 2005 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
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Computing Dictionary

fractal definition

mathematics, graphics
Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot set and Lorenz attractor. Fractals also describe many real-world objects that do not have simple geometric shapes, such as clouds, mountains, turbulence, and coastlines.
Benoit Mandelbrot, the discoverer of the Mandelbrot set, coined the term "fractal" in 1975 from the Latin fractus or "to break". He defines a fractal as a set for which the Hausdorff Besicovich dimension strictly exceeds the topological dimension. However, he is not satisfied with this definition as it excludes sets one would consider fractals.
sci.fractals FAQ (
See also fractal compression, fractal dimension, Iterated Function System.
Usenet newsgroups: news:sci.fractals,,
["The Fractal Geometry of Nature", Benoit Mandelbrot].
[Are there non-self-similar fractals?]
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Example sentences for fractal
The simplified version the wellknown painting software fractal design.
Both strange attractors and julia sets typically have a fractal structure.
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