From: Ben Goertzel (ben@goertzel.org)
Date: Wed Sep 07 2005 - 20:45:41 MDT
> Well, Wolfram's division of cellular automata into
>
> -- stable
> -- periodic
> -- chaotic
> -- complex
>
> led to the notion of "complexity at the edge of chaos", which is the idea
> that in the "parameter space" of CA's, complex CA's are generally found in
> the region of parameter space between the region corresponding to periodic
> CA's and the region corresponding to complex CA's. This rule
> often seems to
> hold for other complex systems besides CA's as well.
This "edge of chaos" thing was introduced in a paper by
Norm Packard and Chris Langton's in the early 1990's, BTW
I published a paper a little before theirs, putting forth a similar idea
(independently conceived), but nobody read it ... boo hoo hoo...
Also, I would add that dynamical systems theory has proved its worth in the
domain of time series analysis. It is the best way to analyze series such
as
EEG or EKG or stock market data. It is able to yield approximate predictive
rules where traditional linear math can't find any patterns at all. This is
how Prediction Company (now part of UBS) made its chaos-theorist founders
Doyne Farmer and Norm Packard wealthy in the 1980's-1990's.
-- ben g
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