  We study emergent dynamics in a viscous drop subject to interfacial nematic
activity. Using hydrodynamic simulations, we show how the interplay of
nematodynamics, activity-driven flows and surface deformations gives rise to a
sequence of self-organized behaviors of increasing complexity, from periodic
braiding motions of topological defects to chaotic defect dynamics and active
turbulence, along with spontaneous shape changes and translation. Our findings
recapitulate qualitative features of experiments and shed light on the
mechanisms underpinning morphological dynamics in active interfaces.
