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Needle models of Laplacian growth.

We consider a simple model to study the competition and screening between branches of anisotropic structures growing in a Laplacian field. Growth conditions are found where the symmetry between the different growing branches is spontaneously broken. In the case of two branches, we obtain an analytic expression for the ratio of the lengths in the stationary regime as a function of the angle between the two needles. We also find that a symmetric pattern with n branches is unstable for ng6 in the simplest diffusion-limited-aggregation-like case. These results are generalized to the more general problem of dielectric breakdown.