  We discuss correlation properties of a general mass density field introducing
a classification of structures based on their complexity. Standard cosmological
models for primordial mass fluctuations are characterized by a sort of
large-scale stochastic order, that we call super-homogeneity to highlight the
fact that mass fluctuations increase as a function of scale in the slowest
possible way for any stochastic mass field. On the other hand the galaxy
spatial distribution show complex structures with a high degree of
inhomogeneity and fractal-like spatial correlations up to some relevant
cosmological scale. The theoretical problem of cosmological structure formation
should then explain the growth of strongly correlated and non-linear structures
from the very uniform field of density fluctuations given as standard initial
condition.
