Morphology of growth by random walk deposition

We simulate a deposition model with a break of symmetry induced by a point source. We find that Tsallis anomalous distribution for random walks n(x)=N(A)/[1+b(q−1)x2]q/(q−1) produces a good fit to the data. We obtain the mean square displacement x2 and the total number of deposited particles N, and compare them to the Gaussian case. Our main conclusions are twofold: first, the parameter q is size dependent; second, long range correlations imply in a violation of the law of great numbers.