From invasion to Eden growth: A family of models for cluster growth in a random environment

We define a family of models to describe cluster growth in random media. These models depend on a temperaturelike parameter and interpolate continuously between the Eden model and the invasion model recently introduced in the study of flow in porous media. Numerical results are presented in two dimensions for a version of these models where growth is biased in a given direction. Directed-invasion clusters are fractal with the same exponents as directed-percolation clusters, but for the other cases studied the clusters are compact. They remain compact even when a "trapping" rule prevents internal holes from being filled.