Model for anisotropic directed percolation

We propose a simulation model to study the properties of directed percolation in two-dimensional anisotropic random media. The degree of anisotropy in the model is given by the ratio μ between the axes of a semiellipse enclosing the bonds that promote percolation in one direction. At percolation, this simple model shows that the average number of bonds per site in two dimensions is an invariant equal to 2.8 independently of μ. This result suggests that Sinai’s theorem proposed originally for isotropic percolation is also valid for anisotropic directed percolation problems. The invariant also yields a constant fractal dimension D_f∼1.71 for all μ, which is the same value found in isotropic directed percolation (i.e., μ=1).