Michael Peters

This music is based on a strange attractor named after Igor Gumowski and Christian Mira, CERN physicists who discovered it during their research in nonlinear dynamical systems.

Starting out with an (x,y) value pair, the next value pair (xn,yn) is computed like this:
xn = a * y + p * x + 2 * sqr(x) * (1 - p) / (1 + sqr(x))
yn = -x + p * xn + 2 * sqr(xn) * (1 - p) / (1 + sqr(xn))
with constant a typically being = 1.0 and p somewhere between -1 and 1.

This process is repeated iteratively, creating more and more value pairs. Each of the value pairs can be mapped to, or drawn as, a pixel on a computer screen. The surprisingly beautiful graphical representations of these attractors seem to resemble plancton lifeforms from some mathematical ocean.

A software that I developed in 1994 could draw many subspecies of these attractors, based on variations of the original iteration formula. It also allowed for realtime manipulation of starting constants, angles, positions, colors, and so forth. Later, I added midi controls, mapping x and y values to pitch and velocity, and some more realtime controls for pitches and scales. The strange attractor software generated music now - algorithmic music, based on nonlinear dynamic systems. Because the attractor parameters could be controlled in realtime, the system could be used for interactive composing.

"Impossible Music" contains 16 recordings of live improvisations with this system. Generated midi data were played by a digital piano and a sampler usually loaded with percussion samples. Most of the improvisations were done together with Matthias Ebbinghaus (who controlled piano pedals and did the live mix).