Numerical results for crossing, spanning and wrapping in two-dimensional percolation

Using a recently developed method to simulate percolation on large clusters of distributed machines, we have numerically calculated crossing, spanning and wrapping probabilities in two-dimensional site and bond percolation with exceptional accuracy. Our results are fully consistent with predictions from conformal field theory. We present many new results that await theoretical explanation, particularly for wrapping clusters on a cylinder. We therefore provide possibly the most up-to-date reference for theoreticians working on crossing, spanning and wrapping probabilities in two-dimensional percolation