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I'm looking for some good books on fractals, with a spin to applications in physics. Specifically, applications of fractal geometry to differential equations and dynamical systems, but with emphasis on the physics, even at the expense of mathematical rigor. Hope that was clear and specific enough.

Emilio Pisanty
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a06e
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    All of renormalization physics is "fractals", in a sense, so this is the entire field of phase transitions, anomalous dimensions, and operator products. It's very big. – Ron Maimon Jun 15 '12 at 17:58
  • @RonMaimon Can you suggest a few references? Preferably books; papers if they are easy to read and can be used as introductions. – a06e Jun 15 '12 at 19:37
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    I like "The Fractal Geometry of Nature", and all of Mandelbrot's books and articles, they are very lucid and full of interesting original ideas. They are also very different from the usual math papers, they are more like physics papers. There is a wonderful small book by Cardy on renormalization theory, and Cardy's papers are classics all, but the papers are not introductory. I think the 1974 Reviews of Modern Physics article by Wilson is readable, but in my memory it requires familiarity with path integrals. Perhaps Kadanoff's papers will work, but they assume you know OPE. not sure. – Ron Maimon Jun 16 '12 at 06:57
  • @RonMaimon Do you mean this book: Scaling and renormalization in statistical physics by John Cardy?. I have it. Do you recommend it? Maybe I'll read it. – a06e Jun 16 '12 at 15:06
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    Yes, that's the one. There is a small issue with condensed matter treatments of this: the field theory intuition is often not as fluent and intuitive as in the high energy treatments, but this is compensated to a degree by the more interesting diverse examples and the explicit calculations. There are also a string of books from the 1980s, an encyclopedic collection by Domb and Green, and a nice little book by Parisi called "statistical field theory" doing the perturbation theory while trying to sidestep explicit epsilon expansion (although I am not sure the result is so great). – Ron Maimon Jun 16 '12 at 17:10

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This answer contains some additional resources that may be useful. Please note that answers which simply list resources but provide no details are strongly discouraged by the site's policy on resource recommendation questions. This answer is left here to contain additional links that do not yet have commentary.

  • Uriel Frisch, Turbulence: the legacy of A.N. Kolmogorov. Cambridge University Press, 1995. 296pp.

  • T. Tél and M. Gruiz, Chaotic Dynamics - An Introduction Based on Classical Mechanics. Cambridge University Press, 2006. 412pp.

  • Edward Ott, Chaos in Dynamical Systems. Cambridge University Press, 1993. A lot of stuff on chaos, but has a good chapter on measuring fractal dimensions in those systems. The language is straightforward.

  • Benoit Mandelbrot, The Fractal Geometry of Nature. Henry Holt and Company, 1983, and all of Mandelbrot's books and articles, they are very lucid and full of interesting original ideas. They are also very different from the usual math papers, they are more like physics papers.

  • There is a wonderful small book by Cardy on renormalization theory [Scaling and Renormalization in Statistical Physics, Cambridge University Press, 1996], and Cardy's papers are classics all, but the papers are not introductory. There is a small issue with condensed matter treatments of this: the field theory intuition is often not as fluent and intuitive as in the high energy treatments, but this is compensated to a degree by the more interesting diverse examples and the explicit calculations.

  • There are also a string of books from the 1980s, an encyclopedic collection by Domb and Green, and a nice little book by Parisi called "statistical field theory" doing the perturbation theory while trying to sidestep explicit epsilon expansion (although I am not sure the result is so great).

  • I think the 1974 Reviews of Modern Physics article by Wilson is readable, but in my memory it requires familiarity with path integrals. Perhaps Kadanoff's papers will work, but they assume you know OPE. not sure.

Credit: Piotr Migdal, user9886, GuySoft, Ron Maimon; from deleted answers and comments.

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Piotr Migdal
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