  We describe a morphological imprint of magnetization found when considering
the relative orientation of the magnetic field direction with respect to the
density structures in simulated turbulent molecular clouds. This imprint was
found using the Histogram of Relative Orientations (HRO): a new technique that
utilizes the gradient to characterize the directionality of density and column
density structures on multiple scales. We present results of the HRO analysis
in three models of molecular clouds in which the initial magnetic field
strength is varied, but an identical initial turbulent velocity field is
introduced, which subsequently decays. The HRO analysis was applied to the
simulated data cubes and mock-observations of the simulations produced by
integrating the data cube along particular lines of sight. In the 3D analysis
we describe the relative orientation of the magnetic field $\mathbf{B}$ with
respect to the density structures, showing that: 1.The magnetic field shows a
preferential orientation parallel to most of the density structures in the
three simulated cubes. 2.The relative orientation changes from parallel to
perpendicular in regions with density over a critical density $n_{T}$ in the
highest magnetization case. 3.The change of relative orientation is largest for
the highest magnetization and decreases in lower magnetization cases. This
change in the relative orientation is also present in the projected maps. In
conjunction with simulations HROs can be used to establish a link between the
observed morphology in polarization maps and the physics included in
simulations of molecular clouds.
