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fractal    音标拼音: [fr'æktəl]
分数维几何,分形

分数维几何,分形

fractal
n 1: (mathematics) a geometric pattern that is repeated at every
scale and so cannot be represented by classical geometry

A fractal is a rough or fragmented
geometric shape that can be subdivided in parts, each of which
is (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 how
close you zoom in).

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
(ftp://src.doc.ic.ac.uk/usenet/usenet-by-group/sci.fractals/)}.

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].

[Are there non-self-similar fractals?]

(1997-07-02)


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英文字典中文字典相关资料:


  • Fractal - Wikipedia
    In mathematics, a fractal is a geometric shape containing detailed structure at arbitrarily small scales, usually having a fractal dimension strictly exceeding the topological dimension
  • What are Fractals? - Fractal Foundation
    Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos Geometrically, they exist in between our familiar dimensions Fractal patterns are extremely familiar, since nature is full of fractals
  • How Fractals Work | HowStuffWorks
    Unconventional 20th-century mathematician Benoit Mandelbrot created the term "fractal" from the Latin word "fractus" (meaning irregular or fragmented) in 1975 You can find this type of irregular and fragmented geometric shape or pattern all around
  • Fractals | Brilliant Math Science Wiki
    So, you might be asking what exactly is a fractal? Well, a fractal, by definition, is a curve or geometric figure, each part of which has the same statistical character as the whole
  • Fractals: Definition and How to Create Them? - GeeksforGeeks
    What Are Fractals? A fractal is a complex geometric shape that can be split into parts, each of which is a reduced-scale copy of the whole This property is known as self-similarity Fractals are typically created by repeating a simple process over and over in an ongoing feedback loop
  • Fractals in Math - Definition, Types, Examples
    Fractal is a pattern that never ends It elaborates mathematical constructs that exhibit self-similarity, meaning they display similar patterns or structures when zoomed in or out
  • Fractal -- from Wolfram MathWorld
    A fractal is an object or quantity that displays self-similarity, in a somewhat technical sense, on all scales The object need not exhibit exactly the same structure at all scales, but the same "type" of structures must appear on all scales
  • Fractal | Mathematics, Nature Art | Britannica
    Fractal, in mathematics, any of a class of complex geometric shapes that commonly have “fractional dimension,” a concept first introduced by the mathematician Felix Hausdorff in 1918
  • Fractal Geometry
    A tutorial on basic fractal geometry and a panorama of uses of fractals, with supporting software, laboratory exercises, and resources for teachers
  • FRACTAL Definition Meaning - Merriam-Webster
    The meaning of FRACTAL is any of various extremely irregular curves or shapes for which any suitably chosen part is similar in shape to a given larger or smaller part when magnified or reduced to the same size





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