Quasi-unit cell description of two-dimensional octagonal quasilattice

We present a cluster covering scheme to construct the two-dimensional Ammann-Beenker tiling with octagonal symmetry. A quasi-unit cell is successfully found which is a two-color cluster similar to Gummelt's two-color decagon in five-fold quasilattice. The quasi-unit cells overlap each other following certain covering rules and thus lead to a perfect octagonal quasilattice.