  Magnetic element tracking is often used to study the transport and diffusion
of the magnetic field on the solar photosphere. From the analysis of the
displacement spectrum of these tracers, it has been recently agreed that a
regime of super-diffusivity dominates the solar surface. Quite habitually this
result is discussed in the framework of fully developed turbulence. But the
debate whether the super-diffusivity is generated by a turbulent dispersion
process, by the advection due to the convective pattern, or by even another
process, is still open, as is the question about the amount of diffusivity at
the scales relevant to the local dynamo process. To understand how such
peculiar diffusion in the solar atmosphere takes places, we compared the
results from two different data-sets (ground-based and space-borne) and
developed a simulation of passive tracers advection by the deformation of a
Voronoi network. The displacement spectra of the magnetic elements obtained by
the data-sets are consistent in retrieving a super-diffusive regime for the
solar photosphere, but the simulation also shows a super-diffusive displacement
spectrum: its competitive advection process can reproduce the signature of
super-diffusion. Therefore, it is not necessary to hypothesize a totally
developed turbulence regime to explain the motion of the magnetic elements on
the solar surface.
