Difference between revisions of "Field:Fractals"

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:* Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.
 
:* Iterated function systems — These have a fixed geometric replacement rule. Cantor set, Sierpinski carpet, Sierpinski gasket, Peano curve, Koch snowflake, Harter-Heighway dragon curve, T-Square, Menger sponge, are some examples of such fractals.
 
:* 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
 
  
*Self-similarity
+
History, Mandelbrot 1975
 +
Self-similarity
 +
Iterating
 +
complex, <math>z = z^2 + c\,</math>
 +
-to zero = black
 +
-infinity - color, how fast is what color
  
*Iterating
+
Fractal dimension
**complex, <math>z = z^2 + c\,</math>
 
***to zero = black
 
***infinity - color, how fast is what color
 
  
*Fractal dimension
+
Examples: Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups.
  
*Examples
+
Nature
**Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups.
 
 
 
*Nature
 
  
 
LINKS
 
LINKS

Revision as of 09:13, 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