[sdiy] State Var Filter with Nonlinear Feedback

[Craig Critchley]

I'm pretty sure it's supposed to be frequency doublings, not wavelength,
though I'm not an expert.

I think nonlinear feedback will generally produce chaos under the right
conditions; cubic feedback used for the Ueda attractor is probably for the
convenience of mathematical analysis.  I know there are other chaotic
circuits that use two diodes for their nonlinear parts.

Does your scope do an X-Y display?  I believe if you hook one axis up to the
LP output and the other up to the BP output, you should get some sort of
"butterfly" pattern when the filter starts becoming chaotic.

I've been wanting to try some chaotic stuff myself; maybe I'll try building
your circuit...

                    ....Craig

----- Original Message -----
From: "Scott Gravenhorst" <music.maker at gte.net>
To: <synth-diy at dropmix.xs4all.nl>
Sent: Thursday, October 18, 2001 6:03 PM
Subject: Re: [sdiy] State Var Filter with Nonlinear Feedback


> Ahhum...,  weakened attractors.  This makes very much sense.
> I've noticed that getting chaotic behavior can be tricky.
> One thing I see in my schematic is a 20K resistor that passes
> a dry version of the feedback signal.  I think there should be
> a 500K to 1meg pot in series with that so that I can better
> control the mix of dry and distorted signal.  This would allow,
> I think, more control over how weak or strong the attractor is.
> Right now, I can change only the level of the distorted version
> of the feedback signal.
>
> grichter at asapnet.net wrote:
> >This is why it is called an "attractor" the function is attracted to
stable
> >points which are numeric multiples. Unstable intervals between the
attractor
> >points are the actual chaotic behavior. A good example is a flute, the
> >"chiff" is chaotic behavior and the tone is when the energy settles into
a
> >stable attractor.
> >
> >It can actually be difficult to get at the chaotic behavior. Depending on
> >the coefficients, the attractors may be so strong, the circuit will not
> >operate in the chaotic mode. A solid tuned pipe has very strong
attractors
> >(tight seal on flute pads) as the pads become leaky, the attractors
become
> >weaker.
> >
> >>
> >> Watching the scope it appears to be 'locking' onto integral harmonics.
> >> A square wave input might be converted to what looks like a square
> >> wave which is amplitude modulated with 2 sine cycles for each 1/2
> >> square cycle.  As you adjust Fc, all of a sudden, 2 sine cycles become
> >> 3, etc.
> >
> >
>
> =========================================================
> - Government: The other religion.
> - The media's credibility should always be questioned.
> - Lambs who lie down with lions are lunch.
>
> -- Scott Gravenhorst | LegoManiac / Lego Trains / RIS 1.5
> -- Linux Rex         | RedWebMail by RedStarWare
> -- FatMan: home1.GTE.NET/res0658s/TekLab_FatMan_WebSite/index.html
>
>