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tokens: be derived. The symbols are the same introduced in the legend of Fig. 8 . In our case, the benefit of using instead of Δα −10, 10 to represent the MFS amplitudes consists of a larger number of useful maps. In Fig. 12 , the versus α 0 plot confirms, based on a larger sample of cases, the trends seen in Fig. 10 . The plot appears less scattered than that of Fig. 10 with regard to positions of Hi-GAL and fBm images, while the positions of the simulations cover a wide range towards larger values. The ‘solenoidal’ and the t 1 , yz maps of both the ‘quasi-hydrodynamical’ and ‘high-magnetization’ scenarios are the closest to the observational points, mostly to the ones corresponding to SPIRE maps of l224 and l217, that is to say that, from the point of view of the MFS amplitude, they show a degree of multifractality similar to that of the most actively star-forming regions in our sample. Figure 12. Plot ot the area A Φ under the MFS and above f = 1.5 versus the peak position α 0 for maps for which A Φ can be derived. The symbols are the same introduced in the legend of Fig. 8 . 4.2.4 Left versus right tail width The diagnostics used in Figs 10 , 11 , and 12 consider the MFS as a whole, neglecting information contained in possible asymmetries. In fact, the left tail of the MFS represents the heterogeneity (broad tail) or uniformity (narrow tail) of the high values distribution, as well as the right tail is related to heterogeneity/uniformity of the low values distribution (e.g. Pavon-Dominguez, Jimenez-Hornero de Rave 2013 ; de Freitas et al. 2017 ). Strong asymmetries are observed in most of the spectra analysed in this paper, with the extreme case represented by PACS 70 maps, discussed above. In order to make use of the MFS asymmetry, single values of α on the two sides of the MFS (for example, α 10 and α −10 , to follow the same approach as above) should be considered (de Freitas et al. 2017 ). In Fig. 13 , the two widths Δα L ≡ α 0 − α 10 and Δα R ≡ α −10 − α 0 , are plotted. First, a strong segregation in abscissa is visible between the group of fBm sets (which are right-skewed and for which the width of the left MFS tail α 10 remains nearly constant, see also Table 3 ) and that of Hi-GAL maps. The latter is internally more composite: the most quiescent, l215, is found on the left while the most active, l224, on the right, as a consequence of the leftward broadening of the MFS in presence of bright compact sources (cf. Fig. 5 ). Along the vertical coordinate, a systematic increase is seen from short to long Herschel wavelengths, while the column density maps appear mixed with SPIRE maps but with no specific trend. Figure 13. Plot ot the MFS left versus right tail amplitude for maps for which it is possible to derive both quantities. The symbols are the same introduced in the legend of Fig. 8 . The dotted line represents the bisector, to facilitate the distinction between left-skewed (below the line) and right-skewed (above the line) MFSs,