An attractor is a set of numerical values, defined by mathematical equations toward which a system tends to evolve, for a wide variety of starting conditions of the system (see wikipedia). There are lots of famous ones, which produce wonderful two or three dimensional graphics; the Lorenz, Rössler, Thomas, Clifford, and many more attractors (e. g.: http://paulbourke.net/fractals/ or attractors animated ) .
Strange or chaotic attractors are actually fairly orderly. Their geometric structures are very often nice and elegant. Even the moving trajectories shows parallelities, similar turns and structures their progression is unpredictable.
How to use these attractors evolvements for musical concepts. In this project, the sound of an attractor is realised by a bunch of 20 sinusoidal tones; their frequencies and loudness‘ are controlled by an attractor’s set of output values. Beside the x, y and z coordinates of the trajectory the speed, the angle changes and the sum-of-all-differences of x, y, and z are generated. For example the angle changes control the loudness›, the speed the mean frequency of the 20 generators and the sum-of-all-differences of x, y, and z their bandwidth. Here are some examples:
A spatialised composition with 4 attractors is «L’océan du son« by Bruno Friedmann (2020).
see entire project «Algorithmic Composing«