  We propose a new statistical model that can reproduce the hierarchical nature
of the ubiquitous filamentary structures of molecular clouds. This model is
based on the multiplicative random cascade, which is designed to replicate the
multifractal nature of intermittency in developed turbulence. We present a
modified version of the multiplicative process where the spatial fluctuations
as a function of scales are produced with the wavelet transforms of a
fractional Brownian motion realisation. This simple approach produces naturally
a log-normal distribution function and hierarchical coherent structures.
Despite the highly contrasted aspect of these coherent structures against a
smoother background, their Fourier power spectrum can be fitted by a single
power law. As reported in previous works using the multiscale non-Gaussian
segmentation (MnGSeg) technique, it is proven that the fit of a single power
law reflects the inability of the Fourier power spectrum to detect the
progressive non-Gaussian contributions that are at the origin of these
structures across the inertial range of the power spectrum. The mutifractal
nature of these coherent structures is discussed, and an extension of the
MnGSeg technique is proposed to calculate the multifractal spectrum that is
associated with them. Using directional wavelets, we show that filamentary
structures can easily be produced without changing the general shape of the
power spectrum. The cumulative effect of random multiplicative sequences
succeeds in producing the general aspect of filamentary structures similar to
those associated with star-forming regions. The filamentary structures are
formed through the product of a large number of random-phase linear waves at
different spatial wavelengths. Dynamically, this effect might be associated
with the collection of compressive processes that occur in the interstellar
medium.
