Fractals and the galaxy distribution
  There is a general agreement that galaxy structures exhibit fractal properties, at least up to some small scale.   However the presence of an eventual crossover towards homogenization, as well as the exact value of the fractal dimension, are still a matter of debate.   I summarize the main points of the this discussion, considering also some galaxy surveys which have recently appeared.   Further I discuss the implications for the standard picture of the observed fractal behaviour in galaxy distribution.   In particular I consider the co-existence of fractal structures and the linear Hubble-law within the same scales. This fact represents a challenge for the standard cosmology where the linear Hubble law is a strict consequence of homogeneity of the expanding universe.   Finally I consider the comparison of CDM-like models with the data noting that the simulations are not able to reproduce the observed properties of galaxy correlations. 
Francesco Sylos Labini