This sounds great, Michael.

I listened to a youtube clip, it sounds like the chaotic behaviour is
somehow related to integer ratio subharmonics, does that make sense ?

Oeyvind

2008/5/1, Michael Gogins <gogins@pipeline.com>:
> I have added two slightly different implementations of Chua's oscillator to
> the list of Csound opcodes. One implementation, chuap, uses a piecewise
> nonlinearity. The other implementation, cuac, uses a cubic polyonimial
> nonlinearity.
>
> Chua's oscillator is the first analog electronic circuit that was proved to
> exhibit chaotic behavior such as bifurcation, chaotic attractors, and so on.
> In the 1990s it was the focus of fairly intensive research and is still
> occasionally used in the context of radio encryption and the like.
>
> There are some videos on YouTube that demonstrate electronic forms of the
> oscillator with Lissajous plots on the oscilloscope and attractive sounds.
>
> The relevance of Chua's oscillator to computer music was explored in some
> papers and demonstrations in the 1990s.
>
> The relevance of Chua's oscillator me personally is that I really like some
> of the sounds I heard on the YouTube clips.
>
> The implementation in Csound also demonstrates the use of the OpcodeBase.hpp
> C++ wrapper for Csound opcodes, and of boost::numeric::ublas for numerical
> computing and digital signal processing. As it happens, there is a MATLAB
> package simulating Chua's oscillator, called ABC++, by James Patrick McEvoy.
> I was able to virtually cut and paste the McEvoy's MATLAB code into C++ code
> because boost::numeric::ublas::vector is coded to be used with the same
> syntax as MATLAB vectors. I suppose this is not likely to be an accident.
> There are probably a number of DSP explorations in MATLAB that could be
> adapted to Csound opcodes this way.
>
> The algorithm uses a difference equation with Runge-Kutta integration to
> simulate the circuit.
>
> I also have booked in an example with 3 sample attractors. This work is not
> finished. I need to improve the example, test the cubic nonlinearity, and
> provide a Python application with sliders to control the parameters for more
> interactive exploration of the oscillator.
>
>
>
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