  We present a variety of structures formed by colloidal droplets at a nematic
liquid crystal-air interface, where the elastic dipole-dipole,
quadrupole-quadrupole, and dipole-quadrupole interactions are all essentially
involved. The colloidal structures observed not only include chains with kinks
or clusters, but also comprise directional structures, such as directional
chains and branches, whose direction is associated with the tilting director in
the liquid crystal layer. The dipole-quadrupole interaction, originating from
the polydispersity of the droplets, plays a central role for the formation of
these directional structures. Clusters consisting of directional branches and
chains are also observed and found to be fractal statistically.
