This paper proposes a constructive approach to creating a method for generating images, which acquires mechanisms to draw images that users provide. The constructive approach relies on a combination of production rules and an optimization technique. The method realized based on the concept of the constructive approach combines simple production rules for cellular automata with a genetic algorithm. The realized method is applied to creating methods for generating simple binary images, and the results show that the proposed approach is capable of acquiring mechanisms to draw given images.