  The evolution and the statistical properties of an infinite gravitating
system represent an interesting and widely investigated subject of research. In
cosmology, the standard approach is based on equations of hydrodynamics. In the
present paper, we analyze the problem from a different perspective, which is
usually neglected. We focus our attention on the fact that at small scale the
distribution is point-like, or granular, and not fluid-like. The basic result
is that the discrete nature of the system is a fundamental ingredient to
understand its evolution. The initial configuration is a Poisson distribution
in which the distribution of forces is governed by the Holtsmark function.
Computer simulations show that the structure formation corresponds to the shift
of the granularity from small to large scales. We also present a simple
cellular automaton model that reproduces this phenomenon.
