Generalization is a perennial issue in evolutionary computation. The ability of evolution to find excellent special-purpose solutions to a problem means that, in some cases, evolutionary techniques generalize poorly. In this study we demonstrate a system that generalizes apoptotic cellular automata rules from a small evaluation arena to a larger one. The generalization preserves many of the features of the cellular automata while increasing the size of the automata’s time-history. The fidelity of the appearance of the generalized rules to their progenitors is high but varies for different progenitors. The generalization is attained by use of single parent techniques. These techniques employ a set of one or more immortal progenitors that are available for crossover but do not otherwise participate in the population. The form of single parent technique used here is novel and the study includes parameter tuning for its use.