Model sets with positive entropy in Euclidean cut and project schemes
  We construct model sets arising from cut and project schemes in Euclidean spaces whose associated Delone dynamical systems have positive toplogical entropy. The construction works both with windows that are proper and with windows that have empty interior. In a probabilistic construction, the entropy almost surely turns out to be proportional to the measure of the boundary of the window. 
Tobias J\"ager, Daniel Lenz and Christian Oertel
math.DS