  We present a new method to study the characteristic scales of collapse and
fragmentation in galactic disks. Clump formation is seeded in simulations via
controlled perturbations with a specified wavelength and velocity. These are
applied to otherwise quiet gas disks ranging from analogues of present day
spirals to gas-rich, high-redshift galaxies. The results are compared to linear
theory, turbulently perturbed disks and observations. The results reflect the
expectations of linear, non-axisymmetric theory with a finite window for growth
into a bound clump. We identify two new modes of clump formation:
rotation-driven fission and fragmentation of tidal tails, though both are
expected to rarely contribute to clump formation in observed disks. We find
that bound clumps are generally much smaller than the so-called Toomre mass.
The preferred scale for fragmentation increases with the disk gas mass but
cannot produce bound objects larger than $\sim10^9$ M$_{\odot}$. The most
likely bound clump mass increases from $3\times10^6$ in low mass disks up to
$5\times10^8$ M$_{\odot}$. We conclude that observed massive stellar and
gaseous clumps on 1 kpc scales at high redshift are most likely aggregates of
many initially distinct bound clumps.
