Journal of Statistical Physics, Vol. 55, Nos. 1/2, 1989, p. 1-28.
We define new tilings of the plane with Robinson triangles, by means of
generalized inflation rules, and study their Fourier spectrum. Penrose's match-
ing rules are not obeyed; hence the tilings exhibit new local environments, such
as three different bond lengths, as well as new patterns at all length scales.
Several kinds of such generalized tilings are considered. A large class of deter-
ministic tilings, including chiral tilings, is strictly quasiperiodic, with a tenfold
rotationally symmetric Fourier spectrum. Random tilings, either locally (with
extensive entropy) or globally random (without extensive entropy), exhibit a
mixed (discrete+continuous) diffraction spectrum, implying a partial perfect
long-range order.