  We investigate the frequency of magnetic activities, namely flux emergence,
splitting, merging, and cancellation, through an automatic detection in order
to understand the generation of the power-law distribution of magnetic flux
reported by Parnell et al. (2009). The quiet Sun magnetograms observed in the
Na I line by Hinode/ SOT is used in this study. Investigated patches range from
10^{17}Mx to 10^{19}Mx. Emergence and cancellation are much less frequent than
merging and splitting. The time scale for splitting is found to be ~33 minutes
and is independent of the flux contained in the splitting patch. Moreover
magnetic patches split into any flux contents with an equal probability. It is
shown that such a fragmentation process leads to a distribution with a
power-law index -2. Merging has a very weak dependence on flux content only
with a power-law index -0.33. These results suggest that 1) magnetic patches
are fragmented by splitting, merging, and tiny cancellation; 2) flux is removed
from the photosphere through tiny cancellations after these fragmentations.
