  Considering quantales as generalised noncommutative spaces, we address as an
example a quantale Pen based on the Penrose tilings of the plane. We study in
general the representations of involutive quantales on those of binary
relations, and show that in the case of Pen the algebraically irreducible
representations provide a complete classification of the set of Penrose tilings
from which its representation as a quotient of Cantor space is recovered.
