  Fortuin-Kastelyn clusters in the critical $Q$-state Potts model are
conformally invariant fractals. We obtain simulation results for the fractal
dimension of the complete and external (accessible) hulls for Q=1, 2, 3, and 4,
on clusters that wrap around a cylindrical system. We find excellent agreement
between these results and theoretical predictions. We also obtain the
probability distributions of the hull lengths and maximal heights of the
clusters in this geometry and provide a conjecture for their form.
