Scaling properties of the Lyman--$\alpha$ forest
  We present some statistical features of the large number of \lya absorption lines detected in high redshift quasar spectra, obtained by using the multifractal approach. In the analysed sample of 12 QSO sight--lines, 11 show scaling behaviour with a crossover between two distinct regimes: a non-homogeneous regime at small scales and a homogeneous regime at large scales. The correlation length shows a redshift dependence, suggesting that the \lya forest can be an intermediate phenomenon between a strongly inhomogeneous galaxy distribution in the local Universe and a homogeneous initial mass distribution. 
S. Savaglio (ESO) and V. Carbone (UNICAL)