  It is known that the gas has a fractal structure in a wide range of spatial
scales with a fractal dimension that seems to be a constant around Df = 2.7. It
is expected that stars forming from this fractal medium exhibit similar fractal
patterns. Here we address this issue by quantifying the degree to which
star-forming events are clumped. We develop, test, and apply a precise and
accurate technique to calculate the correlation dimension Dc of the
distribution of HII regions in a sample of disk galaxies. We find that the
determination of Dc is limited by the number of HII regions, since if there are
< 100 regions available then a bias tending to underestimate the dimension is
produced. The reliable results are distributed in the range 1.5 < Dc < 2.0 with
an average value Dc = 1.81. This corresponds to a three-dimensional dimension
of Df = 2.73, very similar to the value measured in the interstellar clouds.
However, we get significant variations in the fractal dimension among galaxies,
contrary to a universal picture sometimes claimed in literature. The fractal
dimension exhibits a weak but significant correlation with the absolute
magnitude and, to a lesser extent, with the galactic radius. The faintest
galaxies tend to distribute their HII regions in more clustered (less uniform)
patterns. The fractal dimension for the brightest HII regions within the same
galaxy seems to be smaller than for the faintest ones suggesting some kind of
evolutionary efffect, but the obtained correlation remains unchanged if only
the brightest regions are taken into account.
