Is the Universe a fractal? Results from the SSRS2

We perform a fractal analysis of the Southern Sky Redshift Survey 2, following the methods prescribed by Pietronero and collaborators, to check their claim that the galaxy distribution is fractal at all scales, and we discuss and explain the reasons of some controversial points, through tests on both galaxy samples and simulations. We confirm that the amplitude of the two-point correlation function does not depend on the sample depth, but increases with luminosity. We find that there is no contradiction between the results of standard and non-standard statistical analysis; moreover, such results are consistent with theoretical predictions derived from standard CDM models of galaxy formation, and with the hypothesis of homogeneity at large scale ($\sim 100$ \h). However, for our SSRS2 volume-limited subsamples we show that the first zero-point of the autocorrelation function $\xi(s)$ increases linearly with the sample depth, and that its value is comparable to the radius of the maximum sphere which can be completely included in the sampled volume; this implies that the true zero-crossing point of $\xi(s)$ has not been reached. We conclude that the apparent fractal behavior is due to a combination of a luminosity-dependent correlation amplitude and the recovering of power at larger scales in deeper samples.