  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.
