  We compare horizontal velocities, vertical magnetic fields and evolution of
trees of fragmenting granules (TFG, also named families of granules) derived in
the quiet Sun at disk center from observations at solar minimum and maximum of
the Solar Optical Telescope (SOT on board Hinode) and results of a recent 3D
numerical simulation of the magneto-convection. We used 24-hour sequences of a
2D field of view (FOV) with high spatial and temporal resolution recorded by
the SOT Broad band Filter Imager (BFI) and Narrow band Filter Imager (NFI). TFG
were evidenced by segmentation and labeling of continuum intensities.
Horizontal velocities were obtained from local correlation tracking (LCT) of
proper motions of granules. Stokes V provided a proxy of the qline of sight
magnetic field (BLOS). The MHD simulation (performed independently) produced
granulation intensities, velocity and magnetic field vectors. We discovered
that TFG also form in the simulation and show that it is able to reproduce the
main properties of solar TFG: lifetime and size, associated horizontal motions,
corks and diffusive index are close to observations. Largest (but not numerous)
families are related in both cases to strongest flows and could play a major
role in supergranule and magnetic network formation. We found that observations
do not reveal any significant variation of TFG between solar minimum and
maximum.
