  "Cut-out sets" are fractals that can be obtained by removing a sequence of
disjoint regions from an initial region of d-dimensional euclidean space.
Conversely, a description of some fractals in terms of their void complementary
set is possible. The essential property of a sequence of fractal voids is that
their sizes decrease as a power law, that is, they follow Zipf's law. We prove
the relation between the box dimension of the fractal set (in d <= 3) and the
exponent of the Zipf law for convex voids; namely, if the Zipf law exponent e
is such that 1 < e < d/(d-1) and, in addition, we forbid the appearance of
degenerate void shapes, we prove that the corresponding cut-out set has box
dimension d/e (d-1 < d/e < d). We explore the application of this result to the
large scale distribution of matter in cosmology, in connection with ``cosmic
foam'' models.
