  Voronoi tessellations of scale-invariant fractal sets are characterized by
topological and metrical properties that are significantly different from those
of natural cellular structures. As an example we analyze Voronoi diagrams of
intermittent particle distributions generated by a directed percolation process
in (2+1) dimensions. We observe that the average area of a cell increases much
faster with the number of its neighbours than in natural cellular structures
where Lewis' law predicts a linear behaviour. We propose and numerically verify
a universal scaling law that relates shape and size of the cells in
scale-invariant tessellations. A novel exponent, related to the topological
properties of the tessellation, is introduced and estimated numerically.
