  We develop a minimal hydrodynamic model, without an orientational order
parameter, for assemblies of contractile swimmers encapsulated in a droplet of
a binary-fluid emulsion. Our model uses two coupled scalar order parameters,
$\phi$ and $\psi$, which capture, respectively, the droplet interface and the
activity of the contractile swimmers inside this droplet. These order
parameters are also coupled to the velocity field $\bm u$. At low activity, our
model yields a self-propelling droplet whose center of mass $(CM)$ displays
rectilinear motion, powered by the spatiotemporal evolution of the field
$\psi$, which leads to a time-dependent vortex dipole at one end of the
droplet. As we increase the activity, this $CM$ shows chaotic super-diffusive
motion, which we characterize by its mean-square displacement; and the droplet
interface exhibits multifractal fluctuations, whose spectrum of exponents we
calculate. We explore the implications of our results for experiments on active
droplets of contractile swimmers.
