An automaton is described in which growth is regulated by connectivity and a simple self screening constraint. With increased screening, the pattern evolves from compact to one dimensional, passing through a critical state which resembles diffusion-limited aggregation. A finite-size scaling analysis is performed. We propose that this is true critical behavior with the effective temperature determined by the strength of screening. We suggest an order parameter and extract critical exponents. Hyperscaling is discussed. © 1989 The American Physical Society.