This thesis explores the Turing model for pattern formation and its applicationin controlling reaction-diffusion systems. The goal is to simulate both linear andnonlinear reaction-diffusion models, to understand how patterns emerge and toinvestigate the controllability of these systems with boundary controls. Using thefinite difference method (FDM) and other numerical methods on a discretizedgrid, we generated patterns with nonlinear reaction functions, validating Turing’shypothesis that nonlinear models are more applicable for pattern formation. Thenonlinear models produced stable, organized patterns, whereas linear models re-sulted in divergence, creating unrealistic patterns. In the controllability study, wediscovered that full controllability is achieved when all control inputs are active.Our findings suggest that the placement of minimal control inputs, derived fromspecific patterns, ensures full controllability in small systems, though further re-search is needed to generalize this method to larger grids. This work underscoresthe potential of simplified models like Turing’s to provide insights into the com-plex mechanisms governing natural pattern formation.