Eigenvalue spectrum, density of states, and eigenfunctions in a two-dimensional quasicrystal

In this Letter we report the experimental determination of the eigenvalue spectrum, density of states, and individual eigenfunctions in an acoustic system analogous to a two-dimensional Schr\"odinger equation with a quasiperiodic (Penrose tile) potential. The results show features unique to the quasiperiodic symmetry, such as the appearance of gaps and bands with widths which are in the ratio of the golden mean ({}5 +1)/2.