The Voronoi tessellation generated from different distributions of seeds

The Voronoi tessellation in a plane or in a space has recently aroused renewed interest due to its applications in various areas ranging from astrophysics (see refs. [ 1,2 ] ) to the representation of properties of materials (see ref. [ 31). It turns out that some typical parameters like the area distribution in two dimensions and the volume distribution in three dimensions depend strongly on the kind of distribution adopted for the seeds. In particular we will adopt three processes (random, eigenvalues from complex matrices and Sobol) to generate the seeds (see section 2). The adopted probability distribution to lit the normalized histogram of frequencies (the gamma variate, the normal and the lognormal) are described in section 3. The scanning algorithm is presented in section 4, the numerical results are in section 5 and in section 6 we present an astrophysical application.