[sdiy] VC Chaos

[synth at oldmail.charlielamm.com]

Brilliant!  It's guys like Ian, JH and Mike Irwin that keep me thinking 
maybe if I keep soldering some of that brain power might rub off.

On Mon, 27 Sep 2004, Ian Fritz wrote:

> Hi --
> 
> It hasn't been easy to find a way to make a chaos generator suitable for 
> modular synths.  Standard circuits (such as the Chua generator) often 
> require an inductor, have extremely critical adjustments and do not have an 
> obvious means of voltage control.  (Note that I am using chaos in the 
> technical sense, not the common sense of just some kind of noise.)
> 
> A recent paper in the journal "Chaos" describes a general method based on 
> integrator circuits -- basically two integrators and a leaky integrator 
> with gain connected in a loop, with an internal coupling path for a 
> nonlinear element.  It immediately occured to me that this generator would 
> be easy to implement with standard synth VC building blocks, namely two VC 
> integrators, a VCA and a VC lo-pass filter.  It was easy to build this 
> circuit with four OTAs (two LM13600's) and four opamps (two OPA2227's) and 
> to get it working.  I followed the suggestion in the paper of setting the 
> time constants of the lo-pass and one of the integrators to be equal (T1). 
> The second integrator has time constant T2 and the VCA has gain K.  These 
> three parameters are voltage controlled.
> 
> I have put photos of some of the observed phase-space trajectories up on my 
> website.  For these results, T1 and T2 were kept fixed and K was 
> varied.  The first set of photos are plots of one of the output voltages 
> against its first derivative.  Starting at the upper left, the first photo 
> shows a periodic signal (similar to a quadrature oscillator).  The second 
> photo shows the signal after the system has undergone two period 
> doublings.  The third photo demonstrates chaotic oscillations.  As the gain 
> is further increased, the system exhibits several chaotic regions as well 
> as some multiply-periodic fixed orbits.  Finally the system falls back into 
> a regular quadrature oscillation.
> 
> The second set of figures shows the second derivative signal against the 
> first output signal for a number of gain settings.  These are, of course, 
> much more complicated and interesting.
> 
> Here is the link:
> 
> http://home.earthlink.net/~ijfritz/xfer.htm
> 
>    Ian
> 
>