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05 Are fractals and chaos synonymous?




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This article is from the sci.fractals FAQ, by Michael C. Taylor and Jean-Pierre Louvet with numerous contributions by others.

05 Are fractals and chaos synonymous?

No. Many people do confuse the two domains because books or
papers about chaos speak of the two concepts or are illustrated with
fractals.
"Fractals" and "deterministic chaos" are mathematical tools to
modelise different kinds of natural phenomena or objects. "The
keywords in chaos" are impredictability, sensitivity to initial
conditions in spite of the deterministic set of equations describing
the phenomenon.

On the other hand, "the keywords to fractals are self-similarity,
invariance of scale". Many fractals are in no way chaotic (Sirpinski
triangle, Koch curve...).

However, starting from very differents point of view, the two domains
have many things in common : many chaotic phenomena exhibit fractals
structures (in their strange attractors for example... fractal
structure is also obvious in chaotics phenomena due to successive
bifurcations ; see for example the logistic equation Q9 )

The following resources may be helpful to understand chaos:

sci.nonlinear FAQ (UK)
http://www.fen.bris.ac.uk/engmaths/research/nonlinear/faq.html

sci.nonlinear FAQ (US)
http://amath.colorado.edu/appm/faculty/jdm/faq.html

Exploring Chaos and Fractals
http://www.lib.rmit.edu.au/fractals/exploring.html

Chaos and Complexity Homepage (M. Bourdour)
http://www.cc.duth.gr/~mboudour/nonlin.html

The Institute for Nonlinear Science
http://inls.ucsd.edu/

 

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