Stochastic L-systems and quasicrystal patterns

Abstract

Bracketed stochastic Lindenmayer systems (L-systems) are used for the description of certain species of non-deterministic quasicrystal patterns. Several classes of substitution tilings with eight-fold symmetry are introduced. They form the basis for non-deterministic octagonal structures which can be described with stochastic DT0L-systems. Heptagonal structures can also be described with stochastic DT0L-systems, whereas the appropriate scheme for structures with nine-fold symmetry is a stochastic ET0L-system.