Self-Similarity, Fractals, Deterministic Chaos and a New State of Matter

Part of the Springer Series in Information Sciences book series (SSINF, volume 7)


Strange Attractor Golden Ratio Hilbert Curve Fourier Amplitude Spectrum Weierstrass Function 


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Chapter 30

  1. 30.1
    N. J. A. Sloane: AHandb ook of Integer Sequences (Academic Press, Orlando, FL 1973)Google Scholar
  2. 30.2
    D. Shechtman, I. Blech, D. Gratias and J. W. Cahn: Metallic phase with longrange orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)CrossRefADSGoogle Scholar
  3. 30.3
    M. Gardner: Extraordinary nonperiodic tiling that enriches the theory of tiles. Sci. Am. 236, 110–121 (Jan. 1977)CrossRefGoogle Scholar
  4. 30.4
    D. Levine and P. J. Steinhardt: Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53, 2477–2480 (1984)CrossRefADSGoogle Scholar
  5. 30.5
    B. Mandelbrot: The Fractal Geometry of Nature (Freeman, San Francisco 1983)Google Scholar
  6. 30.6
    T. A. Witten and L. M. Sander: Phys. Rev. Lett. 47, 1400–1403 (1981); Phys. Rev. B7, 5686–5697 (1983)CrossRefADSGoogle Scholar
  7. 30.
    7 C. Nicolis and G. Nicolis: Gibt es einen Klima-Attraktor? Phys. Blätter 41, 5–9 (1985)Google Scholar
  8. 30.8
    E. Basar: Toward a physical approach to integrative physiology. I. Brain dynamics and physical causality. Am. J. Physiol. 245 (Regulatory Integrative Comp. Physiol. 14), R510–R533 (1983); see also A. Abraham, A. Mandel and D. Farmer, in Proceedings Nonlinear Functions of the Brain (Santa Barbara 1982)Google Scholar
  9. 30.9
    M. R. Schroeder: Linear prediction, entropy and signal analysis. IEEE ASSP Magazine 1, 3–11 (July 1984)CrossRefGoogle Scholar
  10. 30.10
    M. J. Feigenbaum: Universal behavior in nonlinear systems. Los Alamos Science 1, 4–27 (1981); see also M. J. Feigenbaum: Quantitative universality for a class of nonlinear transformation. J. Statistical Physics 19, 25–52 (1978)MathSciNetGoogle Scholar
  11. 30.11
    M. Schroeder: Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (Freeman, New York 1991)MATHGoogle Scholar

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