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@article{ND_2011_7_1_a9,
author = {G. Nierhaus},
title = {Chaos and self-similarity},
journal = {Russian journal of nonlinear dynamics},
pages = {153--175},
publisher = {mathdoc},
volume = {7},
number = {1},
year = {2011},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ND_2011_7_1_a9/}
}
G. Nierhaus. Chaos and self-similarity. Russian journal of nonlinear dynamics, Tome 7 (2011) no. 1, pp. 153-175. http://geodesic.mathdoc.fr/item/ND_2011_7_1_a9/
[1] Gleick J., Chaos: Making a new science, New York, 1987, 352 pp.
[2] Yorke J. A., Li T. Y., “Period three implies chaos”, Amer. Math. Monthly, 82:10 (1975), 985–992
[3] Poincaré H., Science and method, Dover, New York, 1952, 288 pp.
[4] Mandelbrot B. B., The fractal geometry of nature, W. H. Freeman and Co., New York, 1982, 480 pp.; Mandelbrot B. B., Fraktalnaya geometriya prirody, Institut kompyuternykh issledovanii, M.–Izhevsk, 2002, 656 pp.
[5] Peitgen H.-O., Richter P. H., The beauty of fractals: Images of complex dynamical systems, Springer, Berlin, 1986, 200 pp.
[6] Lindenmayer A., “Mathematical models for cellular interaction in development”, J. Theoret. Biol., 18 (1968), 280–315
[7] Prusinkiewicz P., Lindenmayer A., The algorithmic beauty of plants (The Virtual Laboratory), Springer, New York, 1990, 230 pp.
[8] Hogeweg P., Hesper B., “A model study on biomorphological description”, Pattern Recognition, 6:3-4 (1974), 165–179
[9] Smith A. R., “Plants, fractals, and formal languages”, Computer Graphics, 18 (1984), 1–10
[10] Prusinkiewicz P., Algorithmic Botany, http://algorithmicbotany.org/
[11] Mech R., 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 (Cited 11 Nov 2004), http://algorithmicbotany.org/lstudio/CPFGman.pdf
[12] Mandelbrot B. B., van Ness J. W., “Fractional brownian motions, fractional noises and applications”, SIAM Rev., 10:4 (1968), 422–437
[13] Voss R. F., Clarke J., “$1/f$ noise in music: music from $1/f$ noise”, J. Acoust. Soc. Am., 63:1 (1978), 258–261
[14] Bolognesi T., “Automatic composition: Experiments with self-similar music”, Computer Music Journal, 7:1 (1983), 25–36
[15] Dodge Ch., Jerse Th. A., Computer music: Synthesis, composition, and performance, 2nd ed., Schirmer Books, New York, 1997, 480 pp.
[16] Dodge C., “Profile: A musical fractal”, Computer Music Journal, 12:3 (1988), 10–14
[17] Lang B., Diminuendo: Über selbstähnliche Verkleinerungen, Beiträge zur Elektronischen Musik, 7, Institut für Elektronische Musik (IEM) an der Universität für Musik und darstellende Kunst in Graz, Graz, 1996
[18] Pressing J., “Nonlinear maps as generators of musical design”, Computer Music Journal, 12:2 (1988), 35–46
[19] Bidlack R., “Chaotic systems as simple (but complex) compositional algorithms”, Computer Music Journal, 16:3 (1992), 33–47
[20] Gogins M., “Iterated functions systems music”, Computer Music Journal, 15:1 (1991), 40–48
[21] Leach J., Fitch J., “Nature, music, and algorithmic composition”, Computer Music Journal, 19:2 (1995), 23–33
[22] Prusinkiewicz P., “Score generation with L-systems”, Proc. of the International Computer Music Conference (1986), Intern. Computer Music Ass. San Francisco, 1986, 455–457
[23] McCormack J., “Grammar based music composition”, Complex systems '96: From local interactions to global phenomena, eds. R. Stocker, H. Jelinek, B. Durnota, T. Bossomaier, ISO Press, Amsterdam, 1996, 321–336
[24] DuBois R. L., Applications of generative string-substitution systems in computer music, Dissertation, Columbia University, substitution systems in computer music, 2003
[25] Supper M., “A few remarks on algorithmic composition”, Computer Music Journal, 25:1 (2001), 48–53
[26] Mandelbrot B. B., “Scalebound or scaling shapes: A useful distinction in the visual arts and in the natural sciences”, Leonardo, 14 (1981), 45–47