  We study the dynamical properties of irregular model sets and show that the
translation action on their hull always admits an infinite independence set.
The dynamics can therefore not be tame and the topological sequence entropy is
strictly positive. Extending the proof to a more general setting, we further
obtain that tame implies regular for almost automorphic group actions on
compact spaces. In the converse direction, we show that even in the restrictive
case of Euclidean cut and project schemes irregular model sets may be uniquely
ergodic and have zero topological entropy. This provides negative answers to
questions by Schlottmann and Moody in the Euclidean setting.
