  Results of a statistical analysis of solar granulation are presented. A data
set of 36 images of a quiet Sun area on the solar disk center was used. The
data were obtained with the 1.6 m clear aperture New Solar Telescope (NST) at
Big Bear Solar Observatory (BBSO) and with a broad-band filter centered at the
TiO (705.7 nm) spectral line. The very high spatial resolution of the data
(diffraction limit of 77 km and pixel scale of 0.$"$0375) augmented by the very
high image contrast (15.5$\pm$0.6%) allowed us to detect for the first time a
distinct subpopulation of mini-granular structures. These structures are
dominant on spatial scales below 600 km. Their size is distributed as a power
law with an index of -1.8 (which is close to the Kolmogorov's -5/3 law) and no
predominant scale. The regular granules display a Gaussian (normal) size
distribution with a mean diameter of 1050 km. Mini-granular structures
contribute significantly to the total granular area. They are predominantly
confined to the wide dark lanes between regular granules and often form chains
and clusters, but different from magnetic bright points. A multi-fractality
test reveals that the structures smaller than 600 km represent a multi-fractal,
whereas on larger scales the granulation pattern shows no multi-fractality and
can be considered as a Gaussian random field. The origin, properties and role
of the newly discovered population of mini-granular structures in the solar
magneto-convection are yet to be explored.
