  We study the physical properties derived from interstellar cloud complexes
having a fractal structure. We first generate fractal clouds with a given
fractal dimension and associate each clump with a maximum in the resulting
density field. Then, we discuss the effect that different criteria for clump
selection has on the derived global properties. We calculate the masses, sizes
and average densities of the clumps as a function of the fractal dimension
(D_f) and the fraction of the total mass in the form of clumps (epsilon). In
general, clump mass does not fulfill a simple power law with size of the type
M_cl ~ (R_cl)**(gamma), instead the power changes, from gamma ~ 3 at small
sizes to gamma<3 at larger sizes. The number of clumps per logarithmic mass
interval can be fitted to a power law N_cl ~ (M_cl)**(-alpha_M) in the range of
relatively large masses, and the corresponding size distribution is N_cl ~
(R_cl)**(-alpha_R) at large sizes. When all the mass is forming clumps
(epsilon=1) we obtain that as D_f increases from 2 to 3 alpha_M increases from
~0.3 to ~0.6 and alpha_R increases from ~1.0 to ~2.1. Comparison with
observations suggests that D_f ~ 2.6 is roughly consistent with the average
properties of the ISM. On the other hand, as the fraction of mass in clumps
decreases (epsilon<1) alpha_M increases and alpha_R decreases. When only ~10%
of the complex mass is in the form of dense clumps we obtain alpha_M ~ 1.2 for
D_f=2.6 (not very different from the Salpeter value 1.35), suggesting this a
likely link between the stellar initial mass function and the internal
structure of molecular cloud complexes.
