Posted by
Mike Oliker on
Jun 13, 2005; 2:43pm
URL: http://friam.383.s1.nabble.com/the-Edge-of-Stability-tp520347.html
[I sent this twice: with and without the attached sample of fractal artwork.
Sorry if it gets printed twice.]
After Jonathan Wolfe's presentation to the Albuquerque Complexity Group
(Friam-south?) I got to thinking about the Edge of Chaos. (See Jonathan's
work at the Fractal Foundation:
http://www.fractalfoundation.org/ or see
the attachment. Free Mandelbrot software available for your own creations
there as well).
I've heard of the edge of chaos as a hypothesis: that natural systems are
drawn to the edge of chaos, that it is a point of exceptional fecundity of
behavior, and I've always seen the Mandelbrot Set as a great visualization
of it.
Looking at the Mandelbrot set as Jonathan showed us, from an artist's
perspective, how to navigate and sculpt the resulting artwork, I realized
that it's boundary, where all this infinity of beauty arises, is actually
the Edge of Stability. Chaos (aperiodic orbits) exists within the stable
region in tiny pockets within each "buddha replica" (small echoes of the
whole set). So the edge of the Mandelbrot set is a dense web of
periodicities and behaviors combining chaos and regularity in every part,
all teetering on the edge of instability. It's not the chaos, it's the
instability which kills ya'. In fact, for some purposes, it's chaos that is
the most stable.
The Edge of Stability seems like a better model for evolution -- a small DNA
perturbation jumps one out a distance, often into instability (and death)
but occasionally onto the filaments of stability which arch out from the
edge of the large stable regions. It also highlights why, if one is living
on the edge of stability, one would like a map as to where the stable
regions are.
That may seem like a small distinction, but it is very clarifying for me.
Does it do anything for you?
-Mike Oliker
(PS: ACG meets 2nd and 4th Tuesdays of each month, June 14 is our next
meeting, email me for details or to get on our mailing list)
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