  We consider the limit set in Thurston's compactification PMF of Teichmueller
space of some Teichmueller geodesics defined by quadratic differentials with
minimal but not uniquely ergodic vertical foliations. We show that a) there are
quadratic differentials so that the limit set of the geodesic is a unique
point, b) there are quadratic differentials so that the limit set is a line
segment, c) there are quadratic differentials so that the vertical foliation is
ergodic and there is a line segment as limit set, and d) there are quadratic
differentials so that the vertical foliation is ergodic and there is a unique
point as its limit set. These give examples of divergent Teichmueller geodesics
whose limit sets overlap and Teichmueller geodesics that stay a bounded
distance apart but whose limit sets are not equal. A byproduct of our methods
is a construction of a Teichmueller geodesic and a simple closed curve $\gamma$
so that the hyperbolic length of the geodesic in the homotopy class of gamma
varies between increasing and decreasing on an unbounded sequence of time
intervals along the geodesic.
