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

  • Manfred R. Schroeder
Part of the Springer Series in Information Sciences book series (SSINF, volume 7)

Abstract

Nature abounds with periodic phenomena: from the motion of a swing to the oscillations of an atom, from the chirping of a grasshopper to the orbits of the heavenly bodies. And our terrestrial bodies, too, participate in this universal minuet — from the heart beat to the circadian rhythm and even longer cycles.

Keywords

Hausdorff Dimension Golden Ratio Deterministic Chaos Hilbert Curve Fourier Amplitude Spectrum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 30.1
    N. J. A. Sloane: A Handbook of Integer Sequences ( Academic Press, Orlando, FL, 1973 )MATHGoogle Scholar
  2. 30.2
    D. Shechtman, I. Blech, D. Gratias and J. W. Cahn: Metallic phase with long-range orientational order and no translational symmetry. Phys. Rev. Lett. 53, 1951–1953 (1984)ADSCrossRefGoogle Scholar
  3. 30.3
    M. Gardner: Extraordinary nonperiodic tiling that enriches the theory of tiles. Scientific American 236, 110–121 (Jan. 1977)ADSCrossRefGoogle Scholar
  4. 30.4
    D. Levine and P. J. Steinhardt: Quasicrystals: A new class of ordered structures. Phys. Rev. Lett. 53, 2477–2480 (1984)ADSCrossRefGoogle 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. B 7, 5686–5697 (1983)MathSciNetGoogle Scholar
  7. 30.7
    C. Nicolis and G. Nicolis: Gibt es einen Klima-Attraktor? Phys. Blätter 41, 5–9 (1985)CrossRefGoogle 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);Google Scholar
  9. see also A. Abraham, A. Mandel and D. Farmer, in Proceedings Nonlinear Functions of the Brain (Santa Barbara 1982 )Google Scholar
  10. 30.9
    M. R. Schroeder: Linear prediction, entropy and signal analysis. IEEE ASSP Magazine 1, 3–11 (July 1984)CrossRefGoogle Scholar
  11. 30.10
    M. J. Feigenbaum: Universal behavior in nonlinear systems. Los Alamos Science 1, 427 (1981);MathSciNetGoogle Scholar
  12. see also M. J. Feigenbaum: Quantitative universality for a class of nonlinear transformation. J. Statistical Physics 19, 25–52 (1978)MathSciNetADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Manfred R. Schroeder
    • 1
    • 2
  1. 1.Drittes Physikalisches InstitutUniversität GöttingenGöttingenFed. Rep. of Germany
  2. 2.Acoustics Speech and Mechanics ResearchBell LaboratoriesMurray HillUSA

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