**3.3. Fractal scaling**

The number of neighbors - on average - a galaxy has within a sphere of
radius *r* is just the integral

(4) |

When this function follows a power-law *N*( < *r*)
*r*^{D2},
the exponent is the correlation dimension, and the point pattern
is said to verify fractal scaling. There is no doubt that up to a
given scale the galaxy distribution fits rather well the fractal
picture. However, some controversy regarding the extent of the
fractal regime has motivated an interesting debate
[26,
27,
28,
7].
Nevertheless, the
new data is showing overwhelming evidence that the correlation
dimension is a scale dependent quantity. Different authors
[29,
30,
31,
32,
33,
34,
35,
36,
37]
have analyzed the more recent available redshift surveys using
*N*(*r*) or related measures with appropriate estimators. Their
results show unambiguously an increasing trend of *D*_{2}
with the scale from values of *D*_{2} ~ 2 at intermediate
scales to values of *D*_{2} ~ 3 at scales larger than 30
*h*^{-1} Mpc. Moreover,
one of the strong predictions of the fractal hypothesis is that
the correlation length - the value *r*_{0} at which the
correlation function reaches the unity
((*r*_{0}) = 1) - must increase linearly
with the depth of the sample. This seems not to be the case
[38,
39].