The Hofstadter Butterfly

The Hofstadter butterfly graphically represents the eigenvalues of Harper's equation,

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In the physical world, eigenvalues are the observable energies of a system. Physics dictates that the measured energy of a system is one of its eigenvalues.

The points in the figure above represent the energy levels of charged, massless fermions confined to a plane permeated by a perpendicular magnetic field. Each horizontal slice holds the eigenvalues of the system at a particular magnetic field strength.

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