Sonic Explorations of Gumowski-Mira Maps

This paper studies the use of Gumowski-Mira maps for sonic arts. Gumowski-Mira maps are a set of chaotic systems that produce many organic orbits that resemble cells, flowers and other life forms. This has prompted mathematicians and eventually artists to study them. These maps carry a potential for use in the sonic arts, but until now such use is non-existent. The paper describes two ways of using Gumowski-Mira maps: for synthesis and spatialization. The synthesis approach, which runs in real-time, takes the dynamical system output as the real and imaginary input to an inverse Fourier transformation, thus directly sonifying the algorithm. The spatialization approach uses the shapes of Gumowski-Mira maps as shapes across the acoustic space, using the first 128 iterations of each map as audio particles. The shapes can change based on the maps' initial parameters. The maps are explored in live performance using Leap Motion and Cycling'74's MIRA for iPad as control interfaces of audio processing in SuperCollider. Examples are given in two works, Cells #1 and #2.