This paper describes an introductory computational design course for graduate students of design in which Islamic star patterns are utilized in teaching computational logic and design rules. Formal descriptions of eight pointed Islamic star pattern that depict a variety of geometrical structures and constraints of the Euclidean shapes are extracted with the shape grammar method. Then star pattern generator that runs on a specific CAD system is developed by encoding these formal descriptions in systems scripting language. The examples of new designs are generated, and then fabricated using various CAM technologies.