Abstract
Solutions of chaotic and fractal equations have provided artistically new and interesting classes of images and sounds. Musical scores have been produced from Mandelbrot and Julia set images, and chaotic and fractal techniques have been used to directly synthesize a variety of sound waveforms (see, for example, Monro 1991). One popular approach to sound synthesis is based on Chua's circuit (Mayer-Kress et al. 1993; Mayer-Kress, Choi, and Bargar 1993; Hunt and Johnson 1993). Another method, described here, uses cross-coupled frequency-modulated oscillators (chaotic FM synthesis). Sounds produced by the chaotic FM technique vary from pure sine waves to a variety of complex signals and colored noises. The chaotic FM algorithm includes conventional FM synthesis as a subset. This chaotic FM method can be combined with other chaotic synthesis methods, such as the Ueda attractor, providing an even wider range of sounds. Chaotic synthesis and filtering can be used in both the analog and digital domains, providing similar results. Several examples of chaotic synthesis methods in both domains are provided in this article. The emphasis, however, is on the analog methods, with examples using the Moog modular synthesizer, Buchla electronic musical instruments, and electronic analog computers.
Published Version
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