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Hausdorff dimension of Hofstadter's Butterfly?

  1. May 1, 2014 #1
    Hofstadter's Butterfly (http://en.wikipedia.org/wiki/Hofstadter's_butterfly) is described as a fractal, and in http://physics.technion.ac.il/~odim/hofstadter.html [Broken] it is stated that when the quantum flux is an irrational number of units, then it is a Cantor set, which makes it (by http://en.wikipedia.org/wiki/List_of_fractals_by_Hausdorff_dimension) = ln(2)/ln(3). However, I am wondering whether the statement that it is a Cantor set is perhaps referring to a generalized Cantor set with Hausdorff dimension ln(2)/ ln((1-γ)/2) with perhaps γ depending on the flux?
     
    Last edited by a moderator: May 6, 2017
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  3. May 2, 2014 #2

    Demystifier

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    I think this topic would better fit in some mathematical subforum.
     
  4. May 2, 2014 #3
    Thanks, Demystifier. Should I post this anew in a mathematical subforum, or is there some way to move it? ( I put it in Physics because of the fact that it is the theoretical result of an electron's movement in a strong magnetic field in a crystal.)
     
  5. May 2, 2014 #4

    Doc Al

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    To request that a thread be moved, just use the "Report" button.

    From a physics standpoint, it belongs in Quantum or Solid State. But Demystifier is correct that you'll probably get better answers in a math subforum.

    Let me know which math subforum is most appropriate. (Set theory, Topology, or just General Math.)
     
  6. May 2, 2014 #5
    Thanks, Doc Al. I would be grateful if you could move this to Set Theory.
     
  7. May 2, 2014 #6

    Doc Al

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    Done!
     
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