  We study a model, introduced initially by Gates and Westcott to describe
crystal growth evolution, which belongs to the Anisotropic KPZ universality
class. It can be thought of as a $(2+1)$-dimensional generalisation of the well
known (1+1)-dimensional Polynuclear Growth Model (PNG). We show the full
hydrodynamic limit of this process i.e the convergence of the random interface
height profile after ballistic space-time scaling to the viscosity solution of
a Hamilton-Jacobi PDE: $\partial_tu = v(\nabla u)$ with $v$ an explicit
non-convex speed function. The convergence holds in the strong almost sure
sense.
