Alan Turing explored how patterns emerged in embryos. The modelsexplained by Turing describe how two morphogens interact with eachother and develop certain patterns though different conditions. Usingthe differential equation expressed by Turing gives a lot of freedom inthe choice of variables depending on how the variables are chosen, whichwill be explored and simulated in this thesis. Later, a systems theoreticformulation will be used to explore the stability and controllability ofthe homogenous diffusion problem and Turing’s Reaction and Diffusionproblem. It will be found that under the assumptions made in this thesisboth models will be stable and controllable.