Two-dimensional Voronoi fractal as a sequential fragmentation: The size distribution of fragments

The study of sequential fragmentation dates back to the beginning of the twentieth century when scientists began studying the distribution of particle size as a consequence of a fragmentation process. Since then and for a long time to follow, many empirical functions have been proposed and tested in order to reproduce the fragment size distribution function, among them the most credited is surely that due to Weibull. Not only does the Weibull function often fit the experimental data well, but it has the not negligible property of being the result of a theoretical model proposed by W.K. Brown in the late 1990s. In this paper, we report the numerical results obtained by studying the 2D Voronoi fractal, which can also be considered a sui generis sequential fragmentation model or process. However, the tile area distribution returned by numerical simulations does not fit the Weibull function, whereas the generalized gamma function is an excellent candidate for describing the area distribution after a certain number of tessellations.