Statistical properties and implementation of aperiodic pseudorandom number generators Original Research Article

We discuss the use of quasicrystals in designing deterministic aperiodic pseudorandom number generators. The proposed scheme uses quasicrystals to combine two or three periodic number sequences. We prove that there exists an infinite class of quasicrystals for which the combination scheme (using any nontrivial periodic sequences) produces pseudorandom sequences having no lattice structure. We give empirical results when quasicrystals are used to combine linear congruential generators. Finally, we describe the implementation of two methods for generating quasicrystal points and discuss their respective computational complexities.