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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
  • 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
  • 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
  • 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
  • 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
  • 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
  • What is a Fractal? The Complete Guide to Fractal Geometry
    A fractal is an infinitely complex pattern that repeats at every scale This guide covers everything you need to know about fractal geometry — from nature to mathematics to modern AI
  • 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





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