  We show that any primitive substitution tiling of the plane creates a
separated net which is biLipschitz to the integer lattice. Then we show that if
H is a primitive Pisot substitution in an Euclidean space, for every separated
net Y, that corresponds to some tiling of the tiling space, there exists a
bijection F between Y and the integer lattice that translate every element of Y
a bounded distance. As a corollary we get that we have such an F for any
separated net that corresponds to a Penrose Tiling. The proofs rely on results
of Laczkovich, and Burago and Kleiner.
