A numerical study is made of the spectra of a tight-binding hamiltonian on
square approximants of the quasiperiodic octagonal tiling. Tilings may be pure
or random, with different degrees of phason disorder considered. The level
statistics for the randomized tilings follow the predictions of random matrix
theory, while for the perfect tilings a new type of level statistics is found.
In this case, the first-, second- level spacing distributions are well
described by lognormal laws with power law tails for large spacing. In
addition, level spacing properties being related to properties of the density
of states, the latter quantity is studied and the multifractal character of the
spectral measure is exhibited.Comment: 9 pages including references and figure captions, 6 figures available
upon request, LATEX, report-number els