The structure of invasion percolation clusters in two dimension

We have performed extensive numerical simulations to estimate the fractal dimension of the mass and also the anisotropy in the shape of sample spanning cluster (SSC) in 2-D site invasion percolation processes with and without trapping. In agreement with the most recent works, we have observed that these two different processes belong to two different universality classes. Furthermore, we have determined for the first time, the degree of anisotropy in the shape of SSC by evaluating its gyration ratio. It is found that despite isotropy of the media and also the dynamics, the shape of invasion percolation clusters are not isotropic. The degree of anisotropy is more for clusters of invasion percolation with trapping. We have also studied the distribution of invaded pore sizes for the two invasion percolation processes.