A Geometry Able to Include Mountains and Clouds

  • Benoît Mandelbrot


This chapter originated in ‘A Lecture on Fractals’ delivered at a Nobel Conference at Gustavus Adolphus College in St Peter (Minnesota) in 1990. Mandelbrot’s wide-ranging presentation and the tenor of his responses in the discussion following the lecture demonstrate the ubiquity of fractals, from nature to art and from economics to physics.


Fractal Dimension Fractal Geometry Deterministic Chaos Sierpinski Gasket Equipotential Line 
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Further reading

  1. 1.
    The Fractal Geometry of Nature by B.B. Mandelbrot (W.H. Freeman, 1982) was the first comprehensive book on the subject, and remains a basic reference book. Innumerable other books have appeared since. An up-to date list is found on the website
  2. 2.
    The basic how-to book is The Science of Fractal Images, eds. H.-O. Peitgen and D. Saupe (Springer, 1988).Google Scholar
  3. 3.
    The best-known book on iteration is, deservedly, The Beauty of Fractals by H.-O. Peitgen and P.H. Richter (Springer, 1986).Google Scholar
  4. 4.
    For other aspects of the mathematics, see Fractals: Mathematical Foundations and Applications by K.J. Falconer (Wiley, 1990) and Fractal Geometry and its Applications: a Jubilee of B. Mandelbrot ed. M. Lapidus (2004)Google Scholar

On the concrete uses of fractals, three references are convenient, because they are special volumes of widely available periodicals:

  1. 5.
    Proceedings of the Royal Society of London, Volume A423 (8 May 1989), which was also reprinted as Fractals in the Natural Sciences, ed. M. Fleischmann et al. (Princeton University Press, 1990).Google Scholar
  2. 6.
    Physica D, Volume 38, which was also reprinted as Fractals in Physics, Essays in Honor of B.B. Mandelbrot on his 65th birthday, eds. A. Aharony and J. Feder (North Holland, 1989).Google Scholar
  3. 7.
    Fractals Volume 3 (September 1995), reprinted as Fractal Geometry and Analysis: The Mandelbrot Festschrift, Curação, 1995 eds. C.J.G. Evertsz, H.-O. Peitgen & R.F. Voss.Google Scholar
  4. 8.
    On the physics, a standard textbook is Fractals by J. Feder (Plenum, 1988).Google Scholar

Copyright information

© Springer-Verlag London Limited 2010

Authors and Affiliations

  • Benoît Mandelbrot
    • 1
  1. 1.Thomas B. Watson Research CenterNew YorkUSA

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