AW: the Edge of Chaos

Posted by Bruce Sawhill on Jun 15, 2005; 11:17am
URL: http://friam.383.s1.nabble.com/the-Edge-of-Stability-tp520347p520360.html

"edge of chaos" is defined in terms of correlation length in a system.  
It increases with lambda up to a point, then decreases.  The associated
complexity can be measured by the number of states in a finite state
machine required to produce the output of the system (Crutchfield).  
This gets harder to do for systems more complex than CAs, though.

Bruce


On Jun 15, 2005, at 6:30 AM, Jochen Fromm wrote:

>
> Interesting. Can you define "Edge of Chaos" in terms of chaos theory? I
> think I have seen a definition of edge of chaos somewhere as the point
> right
> before the onset of complete chaos in bifurcation diagrams.
>
> -J.
>
> -----Urspr?ngliche Nachricht-----
> Von: [hidden email] [mailto:[hidden email]] Im
> Auftrag
> von Russell Standish
> Gesendet: Mittwoch, 15. Juni 2005 12:05
> An: The Friday Morning Applied Complexity Coffee Group
> Betreff: Re: [FRIAM] the Edge of Chaos
>
> I would echo Jochen's post somewhat. Edge of chaos is literally true in
> Langton's CAs, which do have a chaotic phase. However, in more general
> evolutionary systems, there appears to be a surface of criticality, on
> one
> side of which lies stability (points or limit cycles), and on the other
> instability, or completely random behaviour. There is no evidence of
> deterministic chaos in this unstable regime, however, so "edge of
> chaos"
> does not seem to be the correct term (although it is often used). My
> own
> preferred term is "self-organised criticality", although for some
> people
> this has its own baggage.
>
>
>
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