[sdiy] What is chaos?

[Ian Fritz]

Hello Paul --

At 03:33 PM 2/12/2007, Paul Perry wrote:
>It is true that chaos functions follow deterministic rules,
>and therefore cannot be called 'random'.
>And so, a chaotic function generated by a digital computer
>gives the same result each time......
>but, in the analog world, this is not so.

Sure, but not even so on a digital computer because of roundoff error.


>Because, in the presence of noise - no matter how little -
>a chaotic system will diverge radically from the 'noiseless'
>predicted pattern. This is an essential property of a
>chaotic system. Which has obvious relevance to e-music.

Yes and no.  True, noise will radically perturb a trajectory.  But imagine 
a small, isolated noise pulse.  This will kick the system off of the 
present trajectory onto a new one.  But both trajectories are still on the 
chaotic attractor, so small noise components (or roundoff errors) 
generally  do not change the overall shape of the attractor.  This was a 
concern in the early days of chaos experiments, but seems pretty well 
accepted by now.


>Most often, when 'music' is constructed from a chaotic
>system, what is beign extracted is a random function
>(well, an apparently random function) of the 1/F type.

Well, maybe in some cases, but that's not my experience (I hope you were 
able to spend some time listening to my demos when they were up).  I can 
clearly see chaotic attractors on the scope trace and trigger musical 
events from them. It is certainly not just 1/f noise.  You can also see 
detailed comparison of observed and predicted chaotic attractors in 
electronic circuits in many places.  Here are several examples with 
side-by-side comparisons.

http://sprott.physics.wisc.edu/pubs/paper245.htm


>http://pear.math.pitt.edu/mathzilla/Examples/chaos/studentReports/JarrodPickens/Chaos.html
>http://ccrma.stanford.edu/~blackrse/chaos.html

Many examples in your references to chaotic music.  If it was all 1/f noise 
it would all sound the same.

   Ian