The Ammann-Beenker tilings revisited
  This paper introduces two tiles whose tilings form a one-parameter family of tilings which can all be seen as digitization of two-dimensional planes in the four-dimensional Euclidean space. This family contains the Ammann-Beenker tilings as the solution of a simple optimization problem. 
Nicolas B\'edaride and Thomas Fernique
math.CO cs.DM