| slovo | definícia |
fractal
(encz) | fractal,fraktál n: Zdeněk Brož |
fractal
(encz) | fractal,fraktální adj: Zdeněk Brož |
fractal
(wn) | fractal
n 1: (mathematics) a geometric pattern that is repeated at every
scale and so cannot be represented by classical geometry |
fractal
(foldoc) | fractal
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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| | podobné slovo | definícia |
fractal geometry
(encz) | fractal geometry, n: |
fractals
(encz) | fractals,fraktály n: pl. Zdeněk Brož |
fractal geometry
(wn) | fractal geometry
n 1: (mathematics) the geometry of fractals; "Benoit Mandelbrot
pioneered fractal geometry" |
fractal compression
(foldoc) | fractal compression
A technique for encoding images using
fractals.
{Yuval Fisher's fractal image compression site
(http://inls.ucsd.edu/y/Fractals/)}.
[Summary?]
(1998-03-27)
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fractal dimension
(foldoc) | fractal dimension
A common type of fractal dimension is the
Hausdorff-Besicovich Dimension, but there are several
different ways of computing fractal dimension. Fractal
dimension can be calculated by taking the limit of the
quotient of the log change in object size and the log change
in measurement scale, as the measurement scale approaches
zero. The differences come in what is exactly meant by
"object size" and what is meant by "measurement scale" and how
to get an average number out of many different parts of a
geometrical object. Fractal dimensions quantify the static
*geometry* of an object.
For example, consider a straight line. Now blow up the line
by a factor of two. The line is now twice as long as before.
Log 2 / Log 2 = 1, corresponding to dimension 1. Consider a
square. Now blow up the square by a factor of two. The
square is now 4 times as large as before (i.e. 4 original
squares can be placed on the original square). Log 4 / log 2
= 2, corresponding to dimension 2 for the square. Consider a
snowflake curve formed by repeatedly replacing ___ with _/\_,
where each of the 4 new lines is 1/3 the length of the old
line. Blowing up the snowflake curve by a factor of 3 results
in a snowflake curve 4 times as large (one of the old
snowflake curves can be placed on each of the 4 segments
_/\_). Log 4 / log 3 = 1.261... Since the dimension 1.261 is
larger than the dimension 1 of the lines making up the curve,
the snowflake curve is a fractal. [sci.fractals FAQ].
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