  Voids are a prominent feature of the galaxy distribution but their
quantitative study is hindered by the lack of a precise definition of what
constitutes a void. Here we propose a definition of voids in point
distributions that uses methods of discrete stochastic geometry, in particular,
Delaunay and Voronoi tessellations, and we construct a new void-finder. We then
apply the void-finder to scaling point distributions. First, we find the voids
of pure fractals with a transition to homogeneity and show that the rank
ordering of the voids also scales (Zipf's law) and, in addition, shows the
transition to homogeneity. However, a pure fractal is arguably not a good model
of the galaxy distribution, so we construct from a cosmological $N$-body
simulation a bifractal mock galaxy sample representing two galaxy populations,
which we identify as "wall" and "field" galaxies. The wall galaxy distribution
fits a pure fractal with a transition to homogeneity and, furthermore, the rank
ordering of its voids shows a scaling range with the right slope plus a
transition to homogeneity.
