Many organisms such as planaria, axolotls and deer exhibit prodigious regenerative abilities, being capable of regenerating complex organs or entire body plans. An understanding of how these organisms store and modify their morphological patterning information is necessary to identify modes of control and intervention. Insight into this process is key to the development of novel biomedical applications. In this work, we present the CANN(k) model: an abstract computational model of pattern regeneration which couples an artificial neural network (ANN) with a k-color cellular automaton (CA). The ANN provides a global information processing system which generates state-dependent update rules for the CA. The CANN(k) models are constructed to generate target patterns which are stable under perturbations of the pattern. We generate ensembles of CANN(4) models for each of the 4-color patterns, assess their sensitivity to changes of the ANN structure. This provides a novel model for understanding the important biological phenomenon of neural control of cellular morphogenesis in development or regeneration.