Difference between revisions of "Field:Fractals"

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:* Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters. --[www.wikipedia.org| Wikipedia]
 
:* Random fractals — Generated by stochastic rather than deterministic processes, for example, trajectories of the Brownian motion, Lévy flight, fractal landscapes and the Brownian tree. The latter yields so-called mass- or dendritic fractals, for example, diffusion-limited aggregation or reaction-limited aggregation clusters. --[www.wikipedia.org| Wikipedia]
  
History, Mandelbrot 1975  
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*History, Mandelbrot 1975  
Self-similarity
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*Self-similarity
Iterating
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**Iterating
complex, <math>z = z^2 + c\,</math>
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**complex, <math>z = z^2 + c\,</math>
-to zero = black
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***to zero = black
-infinity - color, how fast is what color
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***infinity - color, how fast is what color
  
Fractal dimension
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*Fractal dimension
  
Examples: Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups.
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*Examples: Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups.
  
 
Nature
 
Nature

Revision as of 09:14, 1 June 2009


Fractals

A fractal is generally "a rough or fragmented geometric shape that can be split into parts, each of which is (at least approximately) a reduced-size copy of the whole,"[1] a property called self-similarity. The term was coined by Benoît Mandelbrot in 1975 and was derived from the Latin fractus meaning "broken" or "fractured."


  • General description
    • history, self-similarity, iterating


[[Image:|300px|thumb|right|]]

Links to Other Information

Browse Fractals Images

http://en.wikipedia.org/wiki/Fractals