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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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  • 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
  • Fractal Analytics
    Fractal Analytics is a globally recognized enterprise artificial intelligence (AI) company, with a vision to power human decisions in its clients' enterprises by leveraging AI Fractal supports large global enterprises with its end-to-end AI solutions
  • Fractal Audio Systems - Amp Modeling and Effects Processor Technology
    I’ve tried every modelling unit available on this planet and the Fractal is by far miles ahead in every area It’s also proven to be flawlessly dependable in the studio and live performances
  • Fractal Design Gaming PC Hardware
    Fractal Design is a leading designer and manufacturer of premium PC hardware including cases, cooling, power supplies and accessories
  • 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
  • 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
  • Ice Fractal
    As one looks deeper into science, everything becomes increasingly complex and interesting, just like a fractal The simple ideas of multiplication and addition reveal endless complexity in the Mandelbrot set
  • What a Fractal Is and Why You Should Care - Science Notes and Projects
    A fractal is a mathematical equation that displays a repeating pattern, no matter what scale you examine it It can also be described as a pattern of chaos Fractals can be described using mathematical sets, but you also see them all the time in nature
  • Home - Fractal. Institute
    Watch our Introduction Movie to find out what fractals are and why they are important Browse our Encyclopedia if you want to find specific information about a topic Check our News Section for the latest fractal news Create your own fractals with freeware or in your browser
  • 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





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