This project involved investigating Fisher's Equation by reproducing some of the examples in the book, and then finding critical points for a specific example of Fisher's Equation and plotting them. Fisher's equation is \begin{align*} u_t=Du_{xx}+f(u) \end{align*} In this equation, \(f(u)\) is a polynomial based in u. This equation was founded by R.A. Fisher who was a successor of Darwin. He had derived this model for how genes propagate. The reaction part of the equation is the function f, and the diffusion part if \(Du_{xx}\). If homogeneous boundary conditions are used, the constant state is a solution whenever f(C)=0. The equilibrium is stable if f'(c)<0. Each individual part of the project can be seen in the links below.