Quasiperiodic lattices

Abstract

Several methods are currently available for the generation of quasiperiodic lattices in one-, two- and three-dimensions. Many of them are based on the projection from a higher dimensional space. We present simple algorithms for the generation of two-dimensional quasiperiodic lattices with various rotational symmetries. The formalism enables us to describe the quasilattice points in terms of a set of four integers which conform to certain parity conditions. The special case of Pen rose tiling is derived and discussed. The novel algorithm developed by us enables the derivation of an expression for the diffracted intensity from quasiperiodic lattices from first principle without resorting to the higher dimensional formalism.