  We consider a variation of the Hastings-Levitov model HL(0) for random growth
in which the growing cluster consists of two competing regions. We allow the
size of successive particles to depend both on the region in which the particle
is attached, and the harmonic measure carried by that region. We identify
conditions under which one can ensure coexistence of both regions. In
particular, we consider whether it is possible for the process giving the
relative harmonic measures of the regions to converge to a non-trivial ergodic
limit.
