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This paper examines the fitness landscape for evolutionary algorithms evolving cellular automata (CA) rules to satisfy an apoptotic fitness function. This fitness function requires the automata to grow as rapidly as possible and to die out by a fixed time step. The apoptotic CA yielded rules that are extremely robust to variation, while utilizing the majority of available positions in the updating rule. Robustness is assessed by a novel technique called fertility. In addition, fitness morphs are adapted for use on discrete fitness landscapes to demonstrate the localization of high fitness rules to small portions of the fitness landscape. The fitness landscape is shown to be rugose and to be populated by many optima. Single-parent techniques are used both to improve evolutionary techniques for locating automata rules, and to generalize rules that are evolved for one case of the fitness function to other cases of that fitness function. In addition to introducing the evolution of apoptotic CA as a test problem and evolved art technique, many of the analysis tools presented are unique and applicable beyond their focus in the current study.