This article is from the Fractal FAQ, by Ermel Stepp stepp@muvms6.mu.wvnet.edu with numerous contributions by others.

Chaos is apparently unpredictable behavior arising in a deterministic

system because of great sensitivity to initial conditions. Chaos arises in a

dynamical system if two arbitrarily close starting points diverge exponential-

ly, so that their future behavior is eventually unpredictable.

Weather is considered chaotic since arbitrarily small variations in initial

conditions can result in radically different weather later. This may limit

the possibilities of long-term weather forecasting. (The canonical example

is the possibility of a butterfly's sneeze affecting the weather enough to

cause a hurricane weeks later.)

Devaney defines a function as chaotic if it has sensitive dependence on ini-

tial conditions, it is topologically transitive, and periodic points are

dense. In other words, it is unpredictable, indecomposable, and yet contains

regularity.

Allgood and Yorke define chaos as a trajectory that is exponentially unstable

and neither periodic or asymptotically periodic. That is, it oscillates ir-

regularly without settling down.

The following resources may be helpful to understand chaos:

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

http://www.cc.duth.gr/~mboudour/nonlin.html Chaos and Complexity

Homepage (M. Bourdour)

gopher://life.anu.edu.au:70/I9/.WWW/complex_systems/lorenz.gif

Lorenz attractor

http://ucmp1.berkeley.edu/henon.html Experimental interactive

henon attractor

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