Vertex configuration rules to grow an octagonal Ammann–Beenker tiling

Highlights: • We proposed growth rules based on vertex configurations and successfully generated a perfect Ammann–Beenker tiling. • The growth rules determine the local configurations. • The growth rules ensure the distribution of Ammann lines. -- Abstract: Based on vertex configurations in the Ammann–Beenker tiling, we propose an algorithm for aggregation of square and rhombus tiles to generate an octagonal quasilattice, which mimics the growth process of a two-dimensional quasicrystal. Local matching rules with configuration selection are used to guide the way that tiles are joined to a cluster and form Ammann lines according to a generalized Fibonacci sequence. Our results reveal that vertex configuration selection can improve the performance of the algorithm, which provides an approach for growing a perfect octagonal quasiperiodic structure.