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Using Strange Attractors to Model Sound

Sound Engineering Lab, King's College London

Some fractal sounds

Interview for Big Bang, BBC Radio 4, 25-1-1995


Phd Thesis Abstract

This thesis investigates the possibility of applying nonlinear dynamical systems theory to the problem of modelling sound with a computer. The particular interest is in the creative use of sound, where its representation, generation and manipulation are important issues. A specific application, for example, is the modelling of environmental sound for film sound-tracks.

Recently, there have been a number of major advances in the field of nonlinear dynamical systems which include chaos theory and fractal geometry. It is argued that these provide a rich source of ideas and techniques relevant to the issues of modelling sound. One such idea is that complex behaviour may be generated from simple systems. Such behaviour can often replicate a wide range of natural phenomena, or is of interest in its own right because of its aesthetic appeal. This has been demonstrated often through computer generated images and so an equivalent is sought in the audio domain. This work is believed to be the first substantial attempt at this.

The investigation begins with a consideration of fractal and chaotic properties of sound and with a comparison between established approaches to modelling and the alternatives suggested by the new theory. Then, the inquiry concentrates on strange attractors, which are the mathematical objects central to chaos theory, and on two ways in which they may be used to model sound.

The first of these involves using static fractal functions to represent sound time series. A technique is developed for synthesising complex abstract sounds from a small number of parameters. A class of these sounds have the novel property that they are simultaneously rhythms and timbres. It is believed these have potential for use in computer music composition. Also considered is the problem of modelling a given time series with a fractal function. An algorithm for doing this is taken from the literature, shown to be of limited ability, and then improved. The results indicate that data compression may be achieved for certain types of sound.

The second approach focuses on modelling the dynamics of a sound via the embedded reconstruction of an attractor from a time series. Two models are presented, one deterministic, the other stochastic. It is demonstrated that with the first of these, certain sounds may be modelled such that their perceived qualities are preserved. For some other signals, although the sound is not so well preserved, many statistical aspects are. The second model is shown to provide a solution to the film sound-track problem.

It is concluded that this investigation shows strange attractors to have considerable potential as a basis for modelling sound and that there are many areas for continued research.




Mackenzie, J.P. 'Chaotic Predictive Modelling of Sound'. Procs. International Computer Music Conference (ICMC '95), pp 49-56, Banff, Canada, September 1995.

Mackenzie, J.P. and Sandler, M. 'Modelling Sound with Chaos'. Proc. IEEE International Symposium on Circuits and Systems, London, 1994.

Mackenzie, J.P. and Sandler, M. 'Using Chaos to Model Sound'. Proc. IEE Colloquium on Exploiting Chaos in Signal Processing, London, 1994.

Mackenzie, J.P. and Sandler, M. 'Fractal Interpolation Functions for Sound Synthesis'. Procs. Audio Engineering Society 90th Convention, Paris, 1991. Preprint 3008.

Waters, M., Mackenzie, J.P. and Sandler, M. 'Application of Nonlinear Dynamics to Digital Effects for Musical Instruments'. Procs. Audio Engineering Society 90th Convention, Paris, 1991. Preprint 3031.