The spread of infectious disease, virus epidemic, fashion, religion and rumors is strongly affected by the nearest neighbor hence underlying morphologies of the colonies are crucial. Likewise, the morphology of naturally grown patterns ranges from fractal to compact with lacunarity. We analyze the contact process on the fractal clusters simulated by generalized Diffusion-limited Aggregation (g-DLA) model. In g-DLA model, randomly walking particle is added to the cluster with sticking probability [Formula: see text] depending on the local density of occupied sites in the neighborhood of radius [Formula: see text] from the center of active site. It takes values [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) for highly dense, moderately dense and sparsely occupied regions, respectively. The corresponding morphology varies from fractal to compact as [Formula: see text] varies from [Formula: see text] to [Formula: see text]. Interestingly, the contact process on the g-DLA clusters shows clear transition from active phase to absorbing phase and the exponent values fall between 1-d and 2-d in directed percolation (DP) universality class. The local persistence exponents at transition are studied and are found to be much smaller than that for 1-d and 2-d DP cases. We conjecture that infection in the fractal cluster does not easily reach far-flung or remote areas at the periphery of the cluster.
Integrability-preserving regularizations of Laplacian Growth