Doepfer

Subject:  Re: chaos module

Hi Tim,

I know the chaos theory, I have a book on it. It's fascinating
subject, but only until recently I didn't know that they
translated the theory in a famous/notorious module!
I just never heard of those oscillator's you named. 

I also went to a lecture on this subject and it was 
very clearly explained by this professor. I know the chaos
theory orginates from theorectical physics. He had
a simple model with him and demonstrated the how chaos is 
created. He had only a swing which had two wheels attached to it.
First when he moved the swing, it made preditable moves,
but beyond a certain point, totally different things happened
and amazing too see, you couldn't predict any of this 
strange movements anymore. This was the edge of chaos.

Chaos travels from the center to the edge, where it reaches
a point that totally new phenonomen occur. Like your famous 
sample of the butterfly flapping it's wings in North America
can cause a sandstorm in the Sahara. 

Thanks for that great link. What a fine site with glass clear
pictures!!! I have benchmarked in my favourites and when I 
have time and are up to it(oops those maths, but I have to be
cool and don't turn my back on them!). 

Roel 


Hi Roel,

> What the hell are a Chua oscillator and a Duffing oscillator???
> Can you eat it?
> I never heard of this before.
> Most intriquing, please explain!

Tim Wrote:

I have absolutely only a very rough grasp on any of this, but here 
goes. Some of what chaos theory about is how a small change in one 
part of a system can have a large affect on another (a favourite is 
something about a butterfly flapping its wings having an affect half 
way round the world...). It's possible to put together electronic 
circuits that exhibit this kind of behaviour, i.e. a small change 
will suddenly make the circuit jump to a completely different state. 
Chua's circuit is a well known example (named after the guy who first 
made it), Duffing is another, and they are both deceptively very 
simple to look at. They oscillate in strange ways, and changing 
component values by small amounts can completely change this. Chua's 
circuit has many different 'modes' - if I can get the upload to work, 
I'll stick a file in the files area with some plots. In it you'll see 
what is called a 'double scroll', for obvious reasons. Altering the 
pot value can make one half of the scroll disappear; at another it 
goes much larger, called a 'limit cycle' (it sort of saturates). They 
can be made to oscillate at audio frequencies, and the top one of the 
pair looks rather like a square wave through a highly resonant 
filter, and apparently sounds quite interesting. I have a paper where 
they control the oscillator digitally in order to make some decent 
sound (in tune I believe) from it. 

The theory is very mathematical, with lots of heavy differential 
equations in many variables. The 'thing' which make Chua's circuit 
work is what the two op amps do - they emulate a negative resistor (V 
over I through a normal resistor is of course R; V over I for this 
thing gives -R, i.e. has negative gradient!).

And that pretty much sums up all I know. Basically it looks like 
something fun to play with! Just remembered a good website to look at 
is Dan Slater's page:

http://www.nearfield.com/~dan/Music/chaos/Chaosrel.htm

It'll explain it far better than I can, and includes stuff on Buchla 
and references to several good papers.

Cheers,

Tim