Bright light
The Edge of Chaos
I hope the ideas discussed here will throw some light on the
notion of "life evolving to the edge of chaos"  as made
popular by a number of books on complexity.
Often there is a boundary between order and chaotic regions.
In some cases the boundary is relatively simple and clearly defined.
The wellknown bifurcation diagram representing the logistic
map  illustrates the nature of the onset or chaos.
Bifurcation diagram
Here is the graph resulting from iterating x_{n+1} =
a x_{n}(1  x_{n})  and plotting
x_{200} against a .
Ordered and stable states occur on the left. Chaotic and
disordered ones appear on the right  and there is a
transition between them.
Norman Packard coined the idea of "adaptation to the edge of
chaos" [3] in 1988 and Chris Langton
authored papers on the subject in the early 1990s [1,2].
The idea has come in for some criticism [4].
This is references a paper by Melanie Mitchell [5].
The conclusion I tend to draw from Melanie's work is that
Langton's "Lambda" parameter is not terribly useful.
However I think the notion that living systems approach
"the edge of chaos" has at least some remaining utility.
The orderchaos spectrum can be mapped onto the quantity of order
present in the environment  i.e. onto total entropy.
By acting in such a way that entropy increases, living
systems would be pushed away from highly ordered
states  and towards the chaotic region.
They attemt to avoid going into the chaotic regions
 since that represents a zone where all structure is
destroyed.
Thus they gradually take their ecosystem towards "the edge".
References
 Computation at the edge of chaos : Phase transitions and emergent computation  Chris Langton, 1990  Physica D, 42:1237;
 Life at the Edge of Chaos  Chris Langton, 1991  Proceedings of the 2nd Conf. on Artificial Life;
 Adaptation towards the edge of chaos  Norman Packard, 1988, In: Kelso, J. A. S.; Mandell, A. J. & Shlesinger, M. F. (eds.), Dynamic Patterns in Complex Systems, World Scientific. pp. 293;
 ``The Edge of Chaos''
 Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations  Melanie Mitchell, Peter T. Hraber, and James P. Crutchfield, 1993.
Back
tim@tt1.org  http://originoflife.net/
