  The fractal structure of star formation on large scales in disk galaxies is
studied using the size distribution function of stellar aggregates in kpc-scale
star fields. Achival HST images of 10 galaxies are Gaussian smoothed to define
the aggregates, and a count of these aggregates versus smoothing scale gives
the fractal dimension. Fractal and Poisson models confirm the procedure. The
fractal dimension of star formation in all of the galaxies is ~2.3. This is the
same as the fractal dimension of interstellar gas in the Milky Way and nearby
galaxies, suggesting that star formation is a passive tracer of gas structure
defined by self-gravity and turbulence. Dense clusters like the Pleiades form
at the bottom of the hierarchy of structures, where the protostellar gas is
densest. If most stars form in such clusters, then the fractal arises from the
spatial distribution of their positions, giving dispersed star fields from
continuous cluster disruption. Dense clusters should have an upper mass limit
that increases with pressure, from ~1000 Msun in regions like the Solar
neighborhood to one million Msun in starbursts.
