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We present an analysis of probability distribution functions (pdfs) of columndensity in different zones of the star-forming region Perseus and its diffuseenvironment based on the map of dust opacity at 353 GHz available from thePlanck archive. The pdf shape can be fitted by a combination of a lognormalfunction and an extended power-law tail at high densities, in zones centred atthe molecular cloud Perseus. A linear combination of several lognormals fitsvery well the pdf in rings surrounding the cloud or in zones of its diffuseneighbourhood. 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 rathershallow ($\alpha=-0.77\pm0.11$) in the rings delineated around the cloud. Weinterpret these findings as signatures of two distinct physical regimes: i) agravoturbulent one which is characterized by nearly linear scaling of mass andpractical lack of velocity scaling; and ii) a predominantly turbulent one whichis best described by steep velocity scaling and by invariant for compressibleturbulence $\langle\rho\rangle_L u_L^3/L$, describing a scale-independent fluxof the kinetic energy per unit volume through turbulent cascade. Thegravoturbulent spatial domain can be identified with the molecular cloudPerseus while a relatively sharp transition to predominantly turbulent regimeoccurs in its vicinity.

Tracing the general structure of Galactic molecular clouds using Planck data: I. The Perseus region as a test case