We consider the possibility that a substantial fraction of the magnetic fie
ld in the quiet photosphere is generated locally by dynamo action associate
d with the granular and supergranular flows. The argument is based on recen
t advances in the theory of fast dynamos and is supported by large-scale nu
merical simulations that show that thermally driven turbulent convection ca
n indeed be an efficient source of small-scale, highly intermittent magneti
c fields. Some aspects of the resulting magnetic field, such as its strengt
h and degree of intermittency, are discussed.