Energy-level spacing statistics are discussed for the octagonal tiling, a t
wo-dimensional quasiperiodic structure. A recursion relation is written for
the probability distributions of variables defined on finite-size approxim
ants to this quasiperiodic tiling, using their property of similarity under
inflation. Three types of distribution functions are introduced and determ
ined by a combination of numerical and analytical techniques. These are lik
ely to be of general utility in systems lacking translational invariance bu
t with inflation symmetry.