Fractal growth from local instabilities

We study, both with numerical simulations and theoretical methods, a cellul ar automata model for surface growth in the presence of a local instability , driven by an external flux of particles. The growing tip is selected with probability proportional to the local curvature. A probability p of develo ping overhangs through lateral growth is also introduced. For small externa l fluxes, we nd a fractal regime of growth. The value of p determines the f ractal dimension of the aggregate. Furthermore, for each value of p a cross over between two different fractal dimensions is observed. The roughness ex ponent of the aggregates, instead, does not depend on p (chi similar or equ al to 5). A Fixed Scale Transformation (FST) approach is applied to compute theoretically the fractal dimension for one of the branches of the structu re.