>> Iterative systems like nonlinear systems produce remarkable patterns. In
>>mathematics the Mandelbrot set, Julia sets, Sierpinski's gasket and the
>>Duffing equation among others produce amazing complexity (I know Brian Harp
>er
>>you are going to say "ordered" But that is another argument)
>>
>
>Well, I think everyone is probably aware of my objections to using things
>like Mandelbrot or Julia sets as illustrations of complexity. I've been
>thinking a lot about what would be a good yet simple illustration of
>the evolution of complexity. I had thought for some time that a certain
>class of one-dimensional cellular automata (CA) studied extensively by
>Stephen Wolfram (of Mathematica fame) would do the trick. In this type
>of CA (referred to as class IV) one is supposed to observe
>a continual emergence of new patterns for ever, without the more
>common collapse (after some time) into a static or regularly repeating
>pattern. I read a recent paper where the author mentioned another
>work which had proven that no class IV 1-D CA exist. Bummer ;-).
>
What about 2-D class IV 1-D CA? Are they limited?
Let me try again to express why I think that Mandelbrot does fit a complexity
definition. I have not been communicating well what I have been trying to say.
I think I can now express it better. The complexity does not come from the
Mandelbrot set but from an additional feature of the system when one makes
Mandelbrot pictures.
Each picture one can make with a Mandelbrot set is fully defined by the rules
of the Mandelbrot set PLUS four number which represent the xy corners of the
2-D region of the Mandelbrot set. Consider the set of all possible Mandelbrot
pictures. This system of Mandelbrot plus the infinity of regions which can be
magnified creates an infinity of different pictures one can produce from this
system. While the entire mandlebrot set is "ordered" the sum total of
possible pictures is infinite and thus the (mandelbrot+4 numbers) system has a
high algorithmic complexity. The complexity comes not from the Mandelbrot set
but from the 4 numbers used to define each picture. This is what I wonder if
DNA is. The cellular mechanism is like the rules, e.g. the Mandelbrot set.
The unique numbers (which is what the DNA is) define the Picture (morphology)
which the cell creates.
glenn
glenn
Foundation,Fall and Flood
http://members.gnn.com/GRMorton/dmd.htm