  Thurston's boundary to the universal Teichm\"uller space $T(\mathbb{D})$ is
the space $PML_{bdd}(\mathbb{D})$ of projective bounded measured laminations of
$\mathbb{D}$. A geodesic ray in $T(\mathbb{D})$ is of Teichm\"uller type if it
shrinks vertical foliation of an integrable holomorphic quadratic differential.
In a prior work we established that each Teichm\"uller geodesic ray limits to a
multiple (by the reciprocal of the length of the leaves) of vertical foliation
of the quadratic differential.
  Certain non-integrable holomorphic quadratic differential induce geodesic
rays and we consider their limit points in $PML_{bdd}(\mathbb{D})$. Somewhat
surprisingly, the support of the limiting projective measured laminations might
be a geodesic lamination whose leaves are not homotopic to leaves of either
vertical or horizontal foliation of the non-integrable holomorphic quadratic
differential.
