Self-adaptation is used a lot in Evolutionary Strategies and with great success, yet for some reason it is not the mutation adaptation of choice for Genetic Algorithms. This poster describes how a self-adaptive mutation rate was used in a Genetic Algorithms to inverse design behavioral rules for a Cellular Automata. The unique characteristics of this search space gave rise to some interesting convergence behavior that might have implications for using self-adaptive mutation rates in other Genetic Algorithm applications and might clarify why self-adaptation in Genetic Algorithms is less successful than in Evolutionary Strategies. Categories and Subject Descriptors I.2.8 [Computing Methodologies]: ARTIFICIAL INTELLIGENCE—Problem Solving, Control Methods, and Search General Terms Algorithms, Experimentation, Theory Keywords Self Adaptation, Genetic Algorithms, Cellular Automata