Abstract
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.
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Further reading
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 www.math.yale.edu/mandelbrot
The basic how-to book is The Science of Fractal Images, eds. H.-O. Peitgen and D. Saupe (Springer, 1988).
The best-known book on iteration is, deservedly, The Beauty of Fractals by H.-O. Peitgen and P.H. Richter (Springer, 1986).
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)
On the concrete uses of fractals, three references are convenient, because they are special volumes of widely available periodicals:
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).
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).
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.
On the physics, a standard textbook is Fractals by J. Feder (Plenum, 1988).
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Mandelbrot, B. (2010). A Geometry Able to Include Mountains and Clouds. In: Lesmoir-Gordon, N. (eds) The Colours of Infinity. Springer, London. https://doi.org/10.1007/978-1-84996-486-9_3
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