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 . ^ { \prime \prime } 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 .