Definitions for Fractalˈfræk tl

This page provides all possible meanings and translations of the word Fractal

Random House Webster's College Dictionary

frac•talˈfræk tl(n.)

  1. 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.

    Category: Math, Physics

Origin of fractal:

< F fractale < L frāct(us) broken, uneven; term introduced by French mathematician Benoit Mandelbrot (born 1924) in 1975

Princeton's WordNet

  1. fractal(noun)

    (mathematics) a geometric pattern that is repeated at every scale and so cannot be represented by classical geometry

Wiktionary

  1. fractal(Noun)

    A geometric figure which has a Hausdorff dimension which is greater than its topological dimension

  2. fractal(Noun)

    A geometric figure that appears irregular at all scales of length, e.g. a fern.

  3. fractal(Adjective)

    Having the form of a fractal.

  4. Origin: From fractal, from fractus, perfect passive participle of frango.

Freebase

  1. Fractal

    A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers. Fractals are typically self-similar patterns, where self-similar means they are "the same from near as from far". Fractals may be exactly the same at every scale, or, as illustrated in Figure 1, they may be nearly the same at different scales. The definition of fractal goes beyond self-similarity per se to exclude trivial self-similarity and include the idea of a detailed pattern repeating itself. As mathematical equations, fractals are usually nowhere differentiable. An infinite fractal curve can be perceived of as winding through space differently from an ordinary line, still being a 1-dimensional line yet having a fractal dimension indicating it also resembles a surface. The mathematical roots of the idea of fractals have been traced through a formal path of published works, starting in the 17th century with notions of recursion, then moving through increasingly rigorous mathematical treatment of the concept to the study of continuous but not differentiable functions in the 19th century, and on to the coining of the word fractal in the 20th century with a subsequent burgeoning of interest in fractals and computer-based modelling in the 21st century. The term "fractal" was first used by mathematician Benoît Mandelbrot in 1975. Mandelbrot based it on the Latin frāctus meaning "broken" or "fractured", and used it to extend the concept of theoretical fractional dimensions to geometric patterns in nature.

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