Fractal dimensions of confined clusters in two-dimensional directed percolation

The fractal structure of directed permlation clusters, grown at the percolation threshold inside parabolic-l&e systems, is shrdied in two dimensions via Monte Carlo simulations. With a,fe surface at y = fCx' and a dynamical exponent =,.$e surface shape is a relevant permrbation when k < Ilz and, the fractal dimensions of the &isompic clusters vary mntin'nuously with k, Analytic expressions for these variations are obtained using a blob picture approach.