  Extending an example by Colding and Minicozzi, we construct a sequence of
properly embedded minimal disks $\Sigma_i$ in an infinite Euclidean cylinder
around the $x_3$-axis with curvature blow-up at a single point. The sequence
converges to a non smooth and non proper minimal lamination in the cylinder.
Moreover, we show that the disks $\Sigma_i$ are not properly embedded in a
sequence of open subsets of $\mathbb{ R}^3$ that exhausts $\mathbb{ R}^3$.
