  We present an analysis of probability distribution functions (pdfs) of column
density in different zones of the star-forming region Perseus and its diffuse
environment based on the map of dust opacity at 353 GHz available from the
Planck archive. The pdf shape can be fitted by a combination of a lognormal
function and an extended power-law tail at high densities, in zones centred at
the molecular cloud Perseus. A linear combination of several lognormals fits
very well the pdf in rings surrounding the cloud or in zones of its diffuse
neighbourhood. The slope of the mean density scaling law $\langle\rho\rangle_L
\propto L^\alpha$ is steep ($\alpha=-1.93$) in the former case and rather
shallow ($\alpha=-0.77\pm0.11$) in the rings delineated around the cloud. We
interpret these findings as signatures of two distinct physical regimes: i) a
gravoturbulent one which is characterized by nearly linear scaling of mass and
practical lack of velocity scaling; and ii) a predominantly turbulent one which
is best described by steep velocity scaling and by invariant for compressible
turbulence $\langle\rho\rangle_L u_L^3/L$, describing a scale-independent flux
of the kinetic energy per unit volume through turbulent cascade. The
gravoturbulent spatial domain can be identified with the molecular cloud
Perseus while a relatively sharp transition to predominantly turbulent regime
occurs in its vicinity.
