  Numerical simulations of self-gravitating systems are generally based on
N-body codes, which solve the equations of motion of a large number of
interacting particles. This approach suffers from poor statistical sampling in
regions of low density. In contrast, Vlasov codes, by meshing the entire phase
space, can reach higher accuracy irrespective of the density. Here, we
performed one-dimensional Vlasov simulations of a long-standing cosmological
problem, namely the fractal properties of an expanding Einstein-de Sitter
universe in Newtonian gravity. The N-body results were confirmed for
high-density regions and extended to regions of low matter density, where the
N-body approach usually fails.
