  This work examines the relation between the fractal properties of the
photospheric magnetic patterns and those of the coronal magnetic fields in
solar active regions.Our results show no correlation between the fractal
dimensions of the observed 2d photospheric structures and the extrapolated
unstable volumes in the corona, when nonlinear force-free extrapolation is
used. This result is independent of efforts to (1) bring the photospheric
magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the
lower part of the modeled magnetic field volume that is almost completely
filled by unstable volumes. A significant correlation between the fractal
dimensions of the photospheric and coronal magnetic features is only observed
at the zero level (lower limit) of approximation of a current-free (potential)
magnetic field extrapolation. We conclude that the complicated transition from
photospheric non-force-free fields to coronal force-free ones hampers any
direct correlation between the fractal dimensions of the 2d photospheric
patterns and their 3d counterparts in the corona at the nonlinear force-free
limit.
