Scaling properties of planar discrete Poisson-Voronoi tessellations with von Neumann neighborhoods constructed according to the nucleation and growth mechanism.

In contrast to the conventional continual case, discrete Poisson-Voronoi tessellations resulting from the growth to impingement of random nuclei differ from tessellations constructed from the nearest tile loci. Previously studied tessellations were based directly on the notion of locus [A. Korobov, Phys. Rev. E 79, 031607 (2009); A. Korobov, Phys. Rev. E 87, 014401 (2013)]. This paper presents results for tessellations constructed by the growth of random nuclei. Their boundaries have a different structure and scaling properties are comparably more robust. One more scalable characteristic may be introduced for them, the perimeter distribution function, which is well approximated by the normal distribution function with the unit mean and the standard deviation equal to 0.25.