The Fibonacci Quasicrystal
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Ever since their discovery in 1982, quasicrystals have been a topic of high interest in physics. They have many potential application and possess interesting mathematical properties. In this thesis, we investigate one of the most famous quasicrystals: the Fibonacci quasicrystal. We prove mathematically that its energy spectrum has a recursive, Cantor-set like structure, and observe a symmetry in the local density of states. We confirm these predictions with numerical calculations and an experiment on a similar quascrystal.