Difference between revisions of "Field:Fractals"

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|Field=Fractals
 
|Field=Fractals
 
|BasicDesc=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."
 
|BasicDesc=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."
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===Basic Description of Fractals===
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*General description
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**history, self-similarity, iterating
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===Further Information===
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*History
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**Mandelbrot 1975
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*Self-similarity
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*Iterating
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**complex, <math>z = z^2 + c\,</math>
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***to zero = black
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***infinity - color, how fast is what color
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*Fractal dimension
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*Examples
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**Cantor sets, Sierpinski triangle and carpet, Menger sponge, dragon curve, space-filling curve, Koch curve, Lyapunov fractal, and Kleinian groups.
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*Nature
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===Links to Other Information===
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*[http://support1.mathforum.org/~swatimage/Interactive/Puzzle.htm Link to image 1]
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*[http://support1.mathforum.org/~swatimage/Dynamic_Systems/7.htm Link to image 2]
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*[http://mathworld.wolfram.com/Fractal.html Fractal] from Wolfram MathWorld
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*[http://en.wikipedia.org/wiki/Fractal Fractal] from Wikipedia
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|FurtherInfo='''Generating fractals'''
 
|FurtherInfo='''Generating 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]
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|Links=http://en.wikipedia.org/wiki/Fractals
 
|Links=http://en.wikipedia.org/wiki/Fractals
 
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Revision as of 15:01, 29 May 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."


Basic Description of Fractals

  • General description
    • history, self-similarity, iterating


Further Information

  • History
    • Mandelbrot 1975
  • Self-similarity
  • Iterating
    • complex, z = z^2 + c\,
      • 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.
  • Nature

Links to Other Information


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

Links to Other Information

Browse Fractals Images

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