In this paper, a careful mathematical model is built to study the operation of two-dimensional meshes of nearest-neighbor connected processors. This model is then used to show that by replicating the array of processors (by having two layers, each of which is an entire array on its own), it is possible to continue to compute the correct results even if some of the processors are faulty. The basic idea is to avoid faulty processors in the first layer by rerouting the flow of computation through the second layer at all the fault locations. The mathematical model is likely to be useful for proving other results about such cellular arrays as well. The paper is hard to read, however, and figure 4 is missing.