To study the interaction of star-formation and turbulent molecular cloud st
ructuring, we analyse numerical models and observations of self-gravitating
clouds using the Delta -variance as statistical measure for structural cha
racteristics. In the models we resolve the transition from purely hydrodyna
mic turbulence to gravitational collapse associated with the formation and
mass growth of protostellar cores. We compare models of driven and freely d
ecaying turbulence with and without magnetic fields. Self-gravitating super
sonic turbulence always produces a density structure that contains most pow
er on the smallest scales provided by collapsed cores as soon as local coll
apse sets in. This is in contrast to non-self-gravitating hydrodynamic turb
ulence where the Delta -variance is dominated by large scale structures. To
detect this effect in star-forming regions observations have to resolve th
e high density contrast of protostellar cores with respect to their ambient
molecular cloud. Using the 3 mm continuum map of a star-forming cluster in
Serpens we show that the dust emission traces the full density evolution.
On the contrary, the density range accessible by molecular line observation
s is insufficient for this analysis. Only dust emission and dust extinction
observations are able to to determine the structural parameters of star-fo
rming clouds following the density evolution during the gravitational colla
pse.