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)x(2)](q/(q - 1)) produces a good fit to the data. We obt ain the mean square displacement <x(2)> and the total number of deposited p articles nr, and compare them to the Gaussian case. Our main conclusions ar e twofold: first, the parameter q is size dependent; second, long range cor relations imply in a violation of the law of great numbers. (C) 2001 Elsevi er Science B.V. All rights reserved.