  We consider a variation of the standard Hastings-Levitov model HL(0), in
which growth is anisotropic. Two natural scaling limits are established and we
give precise descriptions of the effects of the anisotropy. We show that the
limit shapes can be realised as Loewner hulls and that the evolution of
harmonic measure on the cluster boundary can be described by the solution to a
deterministic ordinary differential equation related to the Loewner equation.
We also characterise the stochastic fluctuations around the deterministic limit
flow.
