Strip method to construct a two-dimensional quasilattice with eight-fold symmetry

Based on the substitution rule and symmetry, we propose a method to generate an octagonal quasilattice consisting of square and rhombus tiles. Local configurations and Ammann lines are used to guide the growth of the tiles in a quasiperiodic order. The structure obtained is a perfect eight-fold symmetric quasilattice, which is confirmed by the radial distribution function and the diffraction pattern.