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fractal    音標拼音: [fr'æktəl]
分數維幾何,分形

分數維幾何,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關資料:
  • Fractal - Wikipedia
    Fractal fluency is a neuroscience model that proposes that, through exposure to nature's fractal scenery, people's visual systems have adapted to efficiently process fractals with ease
  • What are Fractals? - Fractal Foundation
    What are Fractals? A fractal is a never-ending pattern Fractals are infinitely complex patterns that are self-similar across different scales They are created by repeating a simple process over and over in an ongoing feedback loop Driven by recursion, fractals are images of dynamic systems – the pictures of Chaos
  • Fractals | Brilliant Math Science Wiki
    Fractal Dimensions The study of fractals includes measuring scaling properties in a number called the fractal dimension There are several different notions of fractal dimension and here we focus on a notion of fractal dimension for self-similar fractals
  • Fractals: What are They? - Hadron
    Imagine a shape so intricate that it reveals infinite complexity as you zoom in on a structure where patterns repeat endlessly at every scale These mesmerizing forms, known as fractals, defy traditional geometric conventions and open a gateway to understanding natural patterns From the jagged edges of a coastline to the delicate structure of a
  • 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 are distinct from the simple figures of classical, or Euclidean, geometry—the square, the circle, the
  • Mandelbrot Set Fractal Explorer
    Mandelbrot Set Fractal Explorer Click to zoom Right-click to save images, M to make and save a movie of your zoom path z → z2+c is iterated for each complex number c Colors show iterations to divergence; black points converge or cycle Yellow dots show orbits Red dots show limit cycles About iterations This viewer shows more fractal detail over time by refining iterations to infinity
  • 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 Did you know?
  • 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
  • Fractals – Mathigon
    A fractal is a geometric shape that has a fractional dimension Many famous fractals are self-similar, which means that they consist of smaller copies of themselves Fractals contain patterns at every level of magnification, and they can be created by repeating a procedure or iterating an equation infinitely many times
  • Fractals: Definition and How to Create Them? - GeeksforGeeks
    Fractals represent complex mathematical objects that have been extensively studied as well as depicted by mathematicians, artists, and scientists because of their repetitive features Referring to the shapes that are different from the simple geometric forms, fractals possess one unique feature that is called self-similarity, and what this means is that each and every part of it is in some way





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