  We numerically investigate the morphology and disclination line dynamics of
active nematic droplets in three dimensions. Although our model only
incorporates the simplest possible form of achiral active stress, active
nematic droplets display an unprecedented range of complex morphologies. For
extensile activity finger-like protrusions grow at points where disclination
lines intersect the droplet surface. For contractile activity, however, the
activity field drives cup-shaped droplet invagination, run-and-tumble motion or
the formation of surface wrinkles. This diversity of behaviour is explained in
terms of an interplay between active anchoring, active flows and the dynamics
of the motile dislocation lines. We discuss our findings in the light of
biological processes such as morphogenesis, collective cancer invasion and the
shape control of biomembranes, suggesting that some biological systems may
share the same underlying mechanisms as active nematic droplets.
