  Three-dimensional fractal models on grids of 200**3 pixels are generated from
the inverse Fourier transform of noise with a power law cutoff, exponentiated
to give a log normal distribution of density. The fractals are clipped at
various intensity levels and the mass and size distribution functions of the
clipped peaks and their subpeaks are determined. These distribution functions
are analogous to the cloud mass functions determined from maps of the fractal
interstellar medium using various thresholds for the definition of a cloud. The
model mass functions are found to be power laws with powers ranging from -1.6
to -2.4 in linear mass intervals as the clipping level increases from 0.03 to
0.3 of the peak intensity. The low clipping value gives a cloud filling factor
of 0.1 and should be a good model for molecular cloud surveys. The agreement
between the mass spectrum of this model and the observed cloud and clump mass
spectra suggests that a pervasively fractal interstellar medium can be
interpreted as a cloud/intercloud medium if the peaks of the fractal intensity
distribution are taken to be clouds. Their mass function is a power law even
though the density distribution function in the gas is a log-normal. This is
because the size distribution function of the clipped clouds is a power law,
and with clipping, each cloud has about the same average density. A similar
result would apply to projected clouds that are clipped fractals, giving nearly
constant column densities for power law mass functions. The steepening of the
mass function for higher clip values suggests a partial explanation for the
steeper slope of the mass functions for star clusters and OB associations,
which sample denser regions of interstellar gas.
