This paper examines and explores the analytical behavior of two-dimensional (2D) Cellular Automata (CA) rules based on Moore’s neighborhood and different Boolean operators, to better understand rule evolution and its influence on image transformation dynamics. The study investigates both computational and geometrical properties of the patterns generated by CA, revealing that repeated application of both fundamental and derived rules leads to highly regular behavior in finite configurations. Using simple initial setups and nine movement directions of XOR CA, it is possible to understand the development mechanism of Fredkin’s self-replication rules. This work also focuses on the use of 2D uniform and non-uniform periodic boundary conditions in image processing for pattern generation, exploring image formation, replication, multiplication, self-reproduction as well as predicting the number and generation of pattern replicas for other operators like OR, AND, NOR, NAND, etc. The concept of generations and rule sequence is shown to play a critical role in achieving desired image formations.