Abstract
Chaos theory became extremely popular in the 1980s due to a wide adoption of some aspects in the works of Edward N. Lorenz1 and Benoit Mandelbrot2 — the socalled “butterfly effect,” self-similarity or the graphically fascinating illustrations of different fractals became the subjects of a broad non-scientific discussion as well. Regardless of whether the shape of coastlines, the branches of blood vessels or the complex behavior of dynamic systems are represented, chaos theory is occasionally given the significance of a “deus ex machina” — a universal explanation model for complex “natural” structures and processes. The euphoria for this discipline is also reflected by the title of James Gleick’s book “Chaos: Making a New Science,” [6] where the author predicted a paradigm shift in physics evoked by chaos theory.
American meteorologist (1917–2008).
French mathematician of Polish origin, born 1924.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Bidlack R (1992) Chaotic systems as simple (but complex) compositional algorithms. Computer Music Journal, 16/3, 1992
Bolognesi T (1983) Automatic composition: experiments with self-similar music. Computer Music Journal, 7/1, 1983
Dodge C (1988) Profile: a musical fractal. Computer Music Journal, 12/3, 1988
Dodge C, Jerse TA (1997) Computer music: synthesis, composition, and performance, 2nd edn. Schirmer Books, New York. ISBN 0-02-864682-7
DuBois RL (2003) Applications of generative string-substitution systems in computer music. Dissertation. Columbia University, 2003
Gleick J (1987) Chaos: making a new science. Penguin Books, New York. ISBN 0-14-00 9250-1
Gogins M (1991) Iterated function systems music. Computer Music Journal, 15/1, 1991
Hogeweg P, Hesper B (1974) A model study on biomorphological description. Pattern Recognition, 6, 1974
Lang B (1996) Diminuendo. Über selbstähnliche Verkleinerungen. In: Beiträge zur Elektronischen Musik, 7. Institut für Elektronische Musik (IEM) an der Universität für Musik und darstellende Kunst in Graz, Graz.
Leach, J, Fitch J (1995) Nature, music, and algorithmic composition. Computer Music Journal, 19/2, 1995
Lindenmayer A (1968) Mathematical models for cellular interaction in development. Journal of Theoretical Biology, 18, 1968
Mandelbrot B, Van Ness J (1968) Fractional brownian motions, fractional noises and applications. SIAM Review, 10/4
Mandelbrot B (1981) Scalebound or scaling shapes: A useful distinction in the visual arts and in the natural sciences. Leonardo, 14, 1981
Mandelbrot B (1982) The fractal geometry of nature. W. H. Freeman and Company, New York. ISBN 0-7167-1168-9
Mech R (2004) CPFG Version 4.0 User’s Manual based on the CPFG Version 2.7 User’s Manual by Mark James, Mark Hammel, Jim Hanan, Radomir Mech, Przemyslaw Prusinkiewicz with contributions by Radoslaw Karwowski.
McCormack J (1996) Grammar based music composition. In: Stocker R, Jelinek H, Durnota B, Bossomaier T (eds) (1996) Complex systems 96: From local interactions to global phenomena. ISO Press, Amsterdam. ISBN 9-05-199284-X
Peitgen HO, Richter PH (2001) The beauty of fractals. Images of complex dynamical systems. Springer, Berlin. ISBN 978-3540158516
Poincaré H (1952) Science and method. Dover Publications, New York. ISBN 10 0486602214
Pressing J (1988) Nonlinear maps as generators of musical design. Computer Music Journal, 12/2, 1988
Prusinkiewicz P (1986) Score generation with L-systems. In: Proceedings of the 1986 International Computer Music Conference. International Computer Music Association, San Francisco
Prusinkiewicz P, Lindenmayer A (1990) The algorithmic beauty of plants (The Virtual Laboratory). Springer, New York. ASIN 0387972978
Prusinkiewicz P (2004) Algorithmic Botany. http://algorithmicbotany.org/Cited 8 Nov 2004
Smith AR (1984) Plants, fractals, and formal languages. Computer Graphics, 18, 3 July, 1984
Supper M (2001) A few remarks on algorithmic composition. Computer Music Journal 25/1, pages 48–53, 2001
Voss RF, Clarke J (1978) “1/f noise” in music: Music from 1/f noise. Journal of the Acoustical Society of America, 63/1, 1978
Yorke JA, Li TY (1975) Period three implies chaos. The American Mathematical Monthly, 82/10, 1975
Rights and permissions
Copyright information
© 2009 Springer-Verlag/Wien
About this chapter
Cite this chapter
(2009). Chaos and Self-Similarity. In: Algorithmic Composition. Springer, Vienna. https://doi.org/10.1007/978-3-211-75540-2_6
Download citation
DOI: https://doi.org/10.1007/978-3-211-75540-2_6
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-75539-6
Online ISBN: 978-3-211-75540-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)