Listening to the Logistic Map

Andrea Capozucca, Marco Fermani and Simone Giorgini
Proceedings of Bridges 2017: Mathematics, Art, Music, Architecture, Education, Culture
Pages 443–446 Short Papers

Abstract

A logistic map is one of the simplest nonlinear dynamical systems that clearly exhibits a route to chaos. In this paper, we present the creation of a musical piece based on a logistic map. We explored the evolution of the logistic map using a free sonification program called “Music2Chaos”. We divided the one-dimensional interval [0,1] into eleven equal parts, and associated a note of a pentatonic scale to each segment. Every time an iteration took place a corresponding orbit was generated and translated into a sequence of notes. Then, we built up the main theme of the musical piece by choosing the sequences that best express the surprising array of dynamical behaviors of the logistic map, and assembled them according to harmonic rules of music. Time and musical arrangements were chosen to best fit and define the complete song structure.

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