  In the single-scattering theory of electromagnetic radiation, the {\it
fractal regime} is a definite range in the photon momentum-transfer $q$, which
is characterized by the scaling-law behavior of the structure factor: $S(q)
\propto 1/q^{d_f}$. This allows a straightforward estimation of the fractal
dimension $d_f$ of aggregates in {\it Small-Angle X-ray Scattering} (SAXS)
experiments. However, this behavior is not commonly studied in optical
scattering experiments because of the lack of information on its domain of
validity. In the present work, we propose a definition of the
multiple-scattering structure factor, which naturally generalizes the
single-scattering function $S(q)$. We show that the mean-field theory of
electromagnetic scattering provides an explicit condition to interpret the
significance of multiple scattering. In this paper, we investigate and discuss
electromagnetic scattering by three classes of fractal aggregates. The results
obtained from the TMatrix method show that the fractal scaling range is divided
into two domains: 1) a genuine fractal regime, which is robust; 2) a possible
anomalous scaling regime, $S(q) \propto 1/q^{\delta}$, with exponent $\delta$
independent of $d_f$, and related to the way the scattering mechanism uses the
local morphology of the scatterer. The recognition, and an analysis, of the
latter domain is of importance because it may result in significant reduction
of the fractal regime, and brings into question the proper mechanism in the
build-up of multiple-scattering.
