# Fractal Spectra of Operators on Aperiodic Sequences and Tilings

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The Nobel Prize-winning discovery of quasicrystals has spurred much work in aperiodic sequences and tilings. Here, we present numerical experiments conducted by undergraduates at the Summer Math Institute at Cornell under our supervision. Building on our previous work involving one-dimensional discrete Schrodinger operators with potentials given by primitive invertible substitutions on two letters, we present preliminary numerical data on the box-counting dimension and Hausdorff dimension of the spectrum of operators with potentials given by the Thue-Morse sequence and period doubling sequence. We also present preliminary numerical data on the spectrum of the discrete Laplacian on the Penrose tiling and octagonal tiling.