My watch list  

Hofstadter's butterfly

  Hofstadter's Butterfly refers to a fractal discovered by Douglas Hofstadter in his paper "Energy levels and wavefunctions of Bloch electrons in rational and irrational magnetic fields." Hofstadter's Butterfly was the first fractal ever found in physics.

Written while he was at the University of Oregon, this paper was influential in directing further research. Hofstadter predicted that the allowed energy level values of an electron in this crystal lattice, as a function of a magnetic field applied to the system, formed a fractal set. That is, the distribution of energy levels for large scale changes in the applied magnetic field repeat patterns seen in the small scale structure. This fractal structure is generally known as "Hofstadter's butterfly", and has recently been confirmed in transport measurements in two-dimensional electron systems with a superimposed nano-fabricated lattice.[1][2]


  1. ^ "Energy levels and wave functions of Bloch electrons in rational and irrational magnetic fields", Phys. Rev. B 14, 2239 (1976)
  2. ^ The Hofstadter Butterfly
This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Hofstadter's_butterfly". A list of authors is available in Wikipedia.
Your browser is not current. Microsoft Internet Explorer 6.0 does not support some functions on Chemie.DE