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 well-known bifurcation diagram representing the logistic
map - illustrates the nature of the onset or chaos.
Here is the graph resulting from iterating
a xn(1 - xn) - and plotting
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"  in 1988 and Chris Langton
authored papers on the subject in the early 1990s [1,2].
The idea has come in for some criticism .
This is references a paper by Melanie Mitchell .
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 order-chaos 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
Thus they gradually take their ecosystem towards "the edge".
- Computation at the edge of chaos : Phase transitions and emergent computation - Chris Langton, 1990 - Physica D, 42:12-37;
- 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.
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