Fractals, Intermittency and Morphogenesis

  • Bruce J. West
Part of the NATO ASI Series book series (NSSA, volume 138)

Abstract

Until recently, there were no satisfactory models to account for complex physiological structures or processes that do not have characteristic scales of length and/or time. The concept of fractal offers new insights into multiple scaled structures such as the bronchial and coronary tree, His-Purkinje system and chordae tendineae as well as into the broadband, inverse power-law spectra associated with normal electrophysiological dynamics. In a broader biological context the notion of a fractal distribution may have implications regarding error-tolerance and evolution. These ideas are discussed and some supporting mathematical analysis and data are presented.

Keywords

Entropy Lime Dition 

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References

  1. [1]
    T.A. Cook, “The Curves of Life”, Dover, N.Y. (1979); first publ. (1914).Google Scholar
  2. [2]
    H.E. Huntley, “The Divine Proportion”, Dover, N.Y. (1970).Google Scholar
  3. [3]
    D’Arcy Thompson, “On Growth and Form”, Cambridge University Press, (1961); first publ. (1917).Google Scholar
  4. [4]
    B.B. Mandelbrot, “The Fractal Geométry of Nature”, W.H. Freeman and Co., New York (1982).Google Scholar
  5. [5]
    B.J. West and A.L. Goldberger, Am. Sci (in press).Google Scholar
  6. [6]
    B.J. West,“An Essay of the importance of being nonlinear”,Lecture Notes in Biomathematics 62, Springer-Verlag, Berlin (1985).Google Scholar
  7. [7]
    B.J. West, V. Bhargava and A.L. Goldberger, J. Appl. Phys 60:1089 (1986).Google Scholar
  8. [8]
    A.L. Goldberger, V. Bhargava, B.J. West and A.J. Mandell, Biophys.J 48:525 (1985).Google Scholar
  9. [9]
    M. Sernetz, B. Gelléri and J. Hofmann, J. Theor. Biol. 117: 209 (1985).PubMedCrossRefGoogle Scholar
  10. [10]
    A. Babloyantz and A. Destexhe, Proc. Natl. Acad Sci. USA 83: 3513 (1986).CrossRefGoogle Scholar
  11. [11]
    B.B. Mandelbrot, “Fractals, Form, Chance and Dimension”, W.H. Freeman, San Francisco (1977).Google Scholar
  12. [12]
    M.F. Shlesinger, Ann. N.Y Acad. Sci (in press).Google Scholar
  13. C.E. Shannon, Bell System Tech. J 27:379 (1948); ibid. 623 (1948)Google Scholar
  14. [14]
    B.J. West and J. Salk, Eur. J. Oper Res. (in press).Google Scholar
  15. [15]
    E.W. Montroll and B.J. West, in “Fluctuation Phenomena”, eds. E.W. Montroll and J. Lebowitz, North-Holland, Amsterdam (1979); 2nd ed. (1987).Google Scholar
  16. [16]
    E.R. Weibel and D.M. Gomez, Science 137: 577 (1962).Google Scholar
  17. [17]
    E.R. Weibel, “Morphology of the Human Lung”, Academic, New York (1963).Google Scholar
  18. [18]
    O.G. Raabe, H.C. Yeh, G.M. Schum and R.F. Phalen, “Tracheobronchial Geometry: Human, Dog, Rat, Hamster”, Lovelace Found., Albuquerque, New Mexico (1976).Google Scholar
  19. [19]
    D.L. Cohn, Bull. Math. Biophysics 16:59 (1954); ibid 17:219 (1955).Google Scholar
  20. [20]
    P. Glansdorff and I. Prigogine, “Thermodynamic Theory of Structure, Stability and Fluctuation”, Wiley, New York (1971).Google Scholar
  21. [21]
    N. Rashevsky, “Mathematical Biophysics Physico-Mathematical Foundations of Biology”, Vol. 2, 3rd rev. ed., Dover, New York (1960).Google Scholar

Copyright information

© Springer Science+Business Media New York 1987

Authors and Affiliations

  • Bruce J. West
    • 1
  1. 1.Division of Applied Nonlinear ProblemsLa Jolla InstituteLa JollaUSA

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