Certain apparently deterministic physical systems that are described by simple mathematical equations turn out to evolve in chaotic ways. (I use the work "chaotic" in a modern technical sense, meaning that though in principle the future of the system is exactly describable as an evolution of the present - i.e. deterministic - the actual behaviour has an apparent high degree of randomness.) This is a feature of many natural systems, including the dripping of taps and the way that relative numbers of predator and prey species change over time.
In this case, my underlying physical system is based on two gravitational bodies with a small test mass (such as a satellite) orbiting around them. This is well known to exhibit chaotic motion under a wide range of initial conditions. (The initial condition is releasing the test mass somewhere near the system - but not too close to either of the bodies.
In some of the images I have retained an explicit trace of the chaotic motion - though it mainly gets overwritten by the wave motifs.
The other change in the algorithm since my previous experiments involve larger magnitude random variations in the amplitude, phase and colour of the wave motifs, and the use of a Gaussian ("bell curve") probability profile (rather than a more constrained coin toss) in order to control the "random walk" in the system's "phase-space". The general effect is less ordered figures and much stronger motifs (which are somewhat reminiscent of abstract drawings using pastels).
I had meant to put the "wave" stuff aside after "Generate Waves 12", but I wanted to think about using complex dynamics and this was a fairly obvious first experiment - what should have been an easy step. It was, in fact, a good deal more technically challenging than using Lissajous curves because physics does not forgive sloppiness in computing: you have to solve the equations correctly otherwise the results either look obviously wrong, or the algorithm just stops with an error.
