The interests and tendencies of motivations in generated computer graphics between researchers are increased in recent years. There are many various methods for computer graphics in some applications such as architectural arts. In this paper we present two new algorithms for computer generated Islamic Geometrical Patterns, which are 8-ZOHREH and 8-SILI. They are presented as computer algorithms. These algorithms presented and implemented as simple and optimized algorithms. In the proposed algorithms we considered the simple basic rules in geometry such as orthogonal drawing, bisector of angles, and symmetry. The first algorithm generated a main region for 8-ZOHREH in eleven steps and the second algorithm to generate 8-SILI which has twelve steps. Simplicity, robustness, low computational complexity and high speedy are some of the main features of the proposed algorithms. The results of our algorithms are demonstrated in last section.