Substitution tilings with dense tile orientations and n-fold rotational   symmetry
  It is shown that there are primitive substitution tilings with dense tile orientations invariant under n-fold rotation for n=2,3,4,5,6,8. The proof for dense tile orientations uses a general result about irrationality of angles in certain parallelograms. 
Dirk Frettl\"oh, April L.D. Say-awen, M.L.A.N. de las Pe\~nas
math.MG