“A chaotic signal is not a random signal.” I got round to taking a look at Rob Hordijk’s recent Rungler Demo at Modular Meets Leeds 2017, a nice complement to the Mallorca demonstration from 2012.
One detail that I found very interesting was his demonstration of the patterns that can appear within a chaotic signal – the bifurcations or period doublings that can create harmonic partials that are lower in frequency than the signal fed into the filter.1 I’d noticed something like this in James Cigler’s TwinPeak demo yesterday, and had some fun trying it out myself with the filters in my Audulus Blippoo patch.
In essence, since a filter is a feedback system, the moment you apply non-linear feedback, the system automatically becomes potentially chaotic.
I also managed to implement a sample & hold in the Blippoo patch. Hordijk’s inclusion of a S&H in the design is interesting since the Rungler modulations already have something of a S&H character. I take it that including it had something to do with his observation that frequency modulation has a stronger effect when the modulating signal is lower in frequency than the one it is modulating. Using a S&H provided him with a useful device for effectively modulating low frequency periods such as envelopes, for example. In the Blippoo context the S&H definitely seems to add to the chaotic character of the patch rather than simply adding an extra FM modulation band when the modulating oscillator is higher in frequency.
Hans Timmen refers to this on his website: “By using a nonlinear feedback system, patterns are created that exhibit chaotic properties like attractors, bifurcations, etc. Second, the filter also uses a nonlinear feedback system that can go into ranges where bifurcations occur, which results in the creation of ‘undertones’, where the period doublings create harmonic partials that are lower in frequency than the signal fed into the filter.” — Rob Hordijk ↩