Doepfer

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!

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

I've come up with a chaos patch using Doepfer modules sort of based on 
the Wiard Woggle bug diagram. When I figure out how to post it, it'll 
go up on Modular Planet. For those of you who don't have one, I highly 
recommend the Woggle bug - an awesome module that provides both random 
voltages and Forbidden Planet-like audio outs. It's too nifty to 
describe, just get one!

-andrew bunny

From:  "Tim Stinchcombe <timothy@t...>" <timothy@t...> 
Date:  Thu Jan 9, 2003  1:05 am

Subject:  Re: chaos module

Hi Tim and Ethan,

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!

Roel.

Tim wrote:
I wondered this about the Dark Star Chaos myself, so when Blacet 
announced they had a load of the hard-to-get chips at its core, I 
bought one (just the PCB and chip). Haven't built it yet, but from 
the schematic and the chip datasheet, the answer is no, the DSC is 
not associated with what I would regard as 'chaos', i.e. non-linear 
dynamics, Chua's oscillator and the like. However, whether it might 
*sound* like a chaotic oscillator remains to be seen (I doubt it 
though - I did breadboard a Duffing oscillator a while ago, and 
it 'shreiked' rather than 'hissed' noisly!). Basically the DSC is 
voltage-controlled digital noise (like A117), with built in env gen, 
filter, VCA and oscillator.

When I get the time, one of the things I intend doing is to build a 
Chua oscillator, stick a voltage-controlled resistor in it, and see 
what comes out (and if it sounds reasonable, then stick a phase 
comparator and VCO into the mix to see if it can be made to track a 
VCO, PLL style, so that one might be able to play tunes with it...)

Tim