[sdiy] What is chaos?

[Ian Fritz]

At 09:45 AM 2/13/2007, John Mahoney wrote:

>>>Ian, would you say the 3 VCF feedback glorp patch is chaotic or not?
>>
>>[It] could well be, although I'm not exactly sure what the setup 
>>is.  Three VCFs will give you a system of differential equations that is 
>>at least third order, which is the minimum needed.  There also needs to 
>>be an appropriate nonlinearity.
>
>Yeah, not sure why I expected you to know that. Below, then, is the info 
>from Moe himself (it's a reply to a private request from me but I'm sure 
>Dave won't mind).
>--
>john
>
>
>
>Yep, I did the glorp patch, sort of a tribute to RR [Robert Rich]. Here's 
>the link to the original sound:
>http://www.hotrodmotm.com/sounds/glorps.mp3
>
>The post where I explained the patch:
>http://launch.groups.yahoo.com/group/motm/message/26934
>
>And here's the text reproduced:
>
>Re: Glurp without infringement
>
>That patch sounds pretty complex, doesn't it? Nothing could be further 
>from the truth. You are listening to only 3 modules - 2 MOTM-440s and 1 
>MOTM-480.
>
>The 480 adds nothing more than a little swept color to the sound. All the 
>frying sounds, moans, thunder cracks, etc. are generated by the two 440 
>filters oscillating, and feeding each other's FM1 input, which is cranked 
>all the way to -5.
>
>Everything else is just tuning the frequencies until you get an 
>interesting interaction. Because you are using feedback, you can get it to 
>teeter in and out of an unstable situation. You can spend hours conjuring 
>up howls from hell out of this basic simple patch.
>
>Try sticking 3 or more in a feedback loop, using oscillators as well as 
>filters too. When doing this kind of heavy FM, I like to use sine waves as 
>starters because if you use saws or something rich the harmonics can 
>overwhelm you.


John --

Thanks for the reference.  I saw the Rich monkey chatter demo before but 
not this.

It looks like the patch really just relies on two x-coupled 4-pole LPs.  Is 
it chaotic?  Hard to say for sure, but it probably is.

The combination makes an 8th order system, i.e., 8 simultaneous 1st order 
differential equations or one 8th order one.  For chaos you need at least 
3d order plus an appropriate nonlinearity.  I see two nonlinearities here: 
the exponential response of the FM input and the saturation of the gain 
cells from the self-oscillation.

Proving a system to be chaotic can actually be quite a challenge.  The 
present system does not seem to correspond to any standard system analyzed 
before, so there is nothing to compare to.

 From playing around with some 5th order systems, I know that they can 
produce some very complicated repetitive patterns (limit cycles).  So that 
is a possibility here -- to discount it you would have to watch it for a 
long time to make sure there isn't a repetition.  The other thing that can 
happen is that some systems have "transient chaos", a chaotic pattern that 
persists for hundreds of cycles before the system suddenly settles into a 
periodic state.

But either way, it's a great nonlinear system to experiment with.

  Ian