Determining pure discrete spectrum for some self-affine tilings
  By the algorithm implemented in the paper [2] by Akiyama-Lee and some of its predecessors, we have examined the pure discreteness of the spectrum for all irreducible Pisot substitutions of trace less than or equal to $2$, and some cases of planar tilings generated by boundary substitutions due to the paper [17] by Kenyon. 
Shigeki Akiyama, Franz Gaehler, and Jeong-Yup Lee
math.MG