Simulation of three-dimensional bootstrap percolation

On a simple cubic lattie, which is initially occupied randomly with concentration p, a site is emptied if it does not have at least four of its six neighbors occupied. The threshold concentration, below which all sites are emptied after sufficiently many iterations, is found to vary logarithmically with L for L × L × L lattices and L between 32 and 704; it is extrapolated to about 0.936 for infinite lattices. Two other cases are (roughly) compatible with the theoretical prediction of unity as a threshold concentration.