Isn’t de Bruijn’s method specific to Penrose tiles? The aperiodic monotile paper says in section 2 that it is an open question whether the cut-and-project method can construct hat tilings. So de Bruijn would have been no help to solve Simon Tatham’s problem of how to generate hat tile puzzle grids. His two algorithms are the old one his Loopy puzzle uses for Penrose grids, and the new one it uses for hat grids.
yes, agree, but you’re proving my point because as you say the interesting thing about the hats is that they don’t fit into the simple geometric explanation of other aperiodic tilings.
You can play Loopy on a hat tile grid here: https://www.chiark.greenend.org.uk/~sgtatham/puzzles/js/loop...