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fractal
frac·tal F0290000 (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) mathsn (Mathematics) a figure or surface generated by successive subdivisions of a simpler polygon or polyhedron, according to some iterative processadj (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.Thesaurus| 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 |
Translationsfractal
fractal[′frakt·əl] (mathematics) A geometrical shape whose structure is such that magnification by a given factor reproduces the original object. fractal (mathematics, graphics)A fractal is a rough or fragmentedgeometric shape that can be subdivided in parts, each of whichis (at least approximately) a smaller copy of the whole.Fractals are generally self-similar (bits look like the whole)and independent of scale (they look similar, no matter howclose you zoom in).
Many mathematical structures are fractals; e.g. Sierpinski triangle, Koch snowflake, Peano curve, Mandelbrot setand Lorenz attractor. Fractals also describe manyreal-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 theHausdorff Besicovich dimension strictly exceeds thetopological dimension. However, he is not satisfied withthis definition as it excludes sets one would considerfractals.
sci.fractals FAQ.
See also fractal compression, fractal dimension, Iterated Function System.
Usenet newsgroups: news:sci.fractals,news:alt.binaries.pictures.fractals, news:comp.graphics.
["The Fractal Geometry of Nature", Benoit Mandelbrot].
Fractal
A fragmented geometric shape that can be split into parts, each of which approximates a reduced-size copy of the whole, a property which is called self-similarity. Fractals provide the mathematics behind structures in the natural universe—e.g., frost crystals, coastlines, etc.—which cannot be described by the language of euclidean geometry. Fractal analysis is providing new ways to interpret biomedical phenomena. It has been used for classifying histopathology, enzymology, and signal and image compressionFractal
FractalAn object in which the parts are in some way related to the whole. That is, the individual components are "self-similar." An example is the branching network in a tree. While each branch, and each successive smaller branching is different, they are qualitatively similar to the structure of the whole tree.Fractal1. In technical analysis, an indicator of the reversal of the previous trend. It is shown on a candlestick chart as a series of five candles, representing five trading days. A bullish fractal occurs when the lowest low of any trading day is represented by the middle candle, with two successively less low trading days on each side. This is seen as a buy signal. A bearish fractal occurs when the highest high of the five days is represented by the middle candle, with two successively less high trading days on each side. This is seen as a sell signal.
2. Any whole made up of parts that are self-similar.FRACTAL
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fractal
Related to fractal: Fractal dimensionWords related to fractalnoun (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometryRelated Words- pattern
- form
- shape
- math
- mathematics
- maths
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