  Using a simulation technique introduced recently, we study winding clusters
in percolation on the torus and the Moebius strip for different aspect ratios.
The asynchronous parallelization of the simulation makes very large system and
sample sizes possible. Our high accuracy results are fully consistent with
predictions from conformal field theory. The numerical results for the Moebius
strip and the number distribution of winding clusters on the torus await
theoretical explanation. To our knowledge, this study is the first of its kind.
