ON THE PATTERNS OF THE SOLAR GRANULATION AND SUPERGRANULATION

We study the cellular patterns of the white light granulation and of t he chromospheric Ca II K supergranular network. We apply a gradient-ba sed tessellation algorithm to define the cell outlines. The geometry o f the patterns formed by the associated granular and supergranular flo ws are very similar, in spite of the substantial difference in length scale. We compare these patterns to generalized Voronoi foams and conc lude that both convective patterns are very nearly compatible with an essentially random distribution of upflow centers, with the downflow b oundaries determined by the competing strengths of outflows of neighbo ring upwellings. There appears to be a slight clustering in upflow pos itions for the granulation, consistent with the granular evolution. Th is slight preference for large granules to be surrounded by somewhat s maller ones makes the granular and supergranular patterns differ enoug h to allow a correct identification in three out of four cases by eye. The model analogy suggests that the range in outflow strengths is rem arkably small. The patterns appear to be rather insensitive to the det ails of the competing forces that establish the pattern of the downflo w network: similar patterns result under very different conditions, so that little can be learned about the details of the forces involved b y studying the geometry of these patterns only.