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Working paper

Ammann tilings: a classification and an application

Durand B., Shen A., Vereshchagin N.
We describe all Ammann tilings of a plane, a half-plane and a quadrant. In our description, every tiling is associated to an infinite sequence of two letters. We provide simple criteria of (a) whether a tiling associated with a sequence tiles the entire plane, a half-plane or a quadrant and (b) whether tiling associated with two sequences are congruent. It is well known that all Ammann tilings are aperiodic; we show how one can use this fact to construct an aperiodic 2-dimensional sub-shift of finite type