page_title: Hofstadter's butterfly
hierarchical_section_title: Hofstadter's butterfly
caption_attribution_description: English: A colored Hofstadter butterfly. The phase diagram of Chern numbers in a model of the Quantum Hall effect.
context_page_description: In condensed matter physics, Hofstadter's butterfly describes the spectral properties of non-interacting two-dimensional electrons in a magnetic field. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of computer graphics. The name reflects the visual resemblance of the figure on the right to a swarm of butterflies flying to infinity.
  The Hofstadter butterfly plays an important role in the theory of the integer quantum Hall effect, and David J. Thouless won the Nobel Prize in physics in 2016 for the discovery that the wings of the butterfly are characterized by Chern integers, the quantized Hall conductances discovered in 1980 by Klaus von Klitzing for which he won the Nobel Prize in 1985. The colors in the diagram reflect the different Chern numbers.
context_section_description: In condensed matter physics, Hofstadter's butterfly describes the spectral properties of non-interacting two-dimensional electrons in a magnetic field. The fractal, self-similar nature of the spectrum was discovered in the 1976 Ph.D. work of Douglas Hofstadter and is one of the early examples of computer graphics. The name reflects the visual resemblance of the figure on the right to a swarm of butterflies flying to infinity.
  The Hofstadter butterfly plays an important role in the theory of the integer quantum Hall effect, and David J. Thouless won the Nobel Prize in physics in 2016 for the discovery that the wings of the butterfly are characterized by Chern integers, the quantized Hall conductances discovered in 1980 by Klaus von Klitzing for which he won the Nobel Prize in 1985. The colors in the diagram reflect the different Chern numbers.
caption: Colored Hofstadter's butterfly: The colors represent the Chern numbers of the gaps in the spectrum, aka the TKNN integers.
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