Information theory is used to study the effects of screening on the rate of entropy production during pattern formation. Screening is an effect where the outermost parts of a growing fractal pattern influence the growth probability at interior sites. The results demonstrate that a state of maximum entropy production does exist for dynamical systems which generate patterns based on simple screening rules alone. This state corresponds to a critical point where the pattern exhibits self-similarity and fractal properties typical of random aggregates. Scaling occurs because the screening transmits information from the smallest to the largest scales of the system. © 1989 Plenum Publishing Corporation.