Comparison of two algorithms for bootstrap percolation models

Two different algorithms for determining the percolation threshold in bootstrap percolation models are compared. One algorithm is the usual literal bootstrap prescription, whereby each site with less than the required number of neighbours, is removed by a repetitive culling process. The second algorithm was proposed for diffusion percolation models, and has some similarities with multigrid or Swendsen-Wang algorithms for thermal systems, since it considers entire clusters in a single step. It is called the rectangle algorithm, because the clusters of the models under investigation are compact. For small systems and concentrations where not all lattices percolate, the literal algorithm is more efficient. However, there is some indication that for large systems and concentrations closer to the threshold value of the infinite system, the rectangle algorithm is faster. This has interesting implications for calculations in some other cellular automata systems.