  Spectra of suitably chosen Pisot-Vijayaraghavan numbers represent non-trivial
examples of self-similar Delone point sets of finite local complexity,
indispensable in quasicrystal modeling. For the case of quadratic Pisot units
we characterize, dependingly on digits in the corresponding numeration systems,
the spectra which are bounded distance to an average lattice. Our method stems
in interpretation of the spectra in the frame of the cut-and-project method.
Such structures are coded by an infinite word over a finite alphabet which
enables us to exploit combinatorial notions such as balancedness, substitutions
and the spectrum of associated incidence matrices.
