The purpose of this project is to create a tool to help visualize and gain intuition for conformal mappings of the complex plane.
The goal of the first stage is simple: we put a bitmap on the image, or w-plane. We then choose a conformal map parameterized by a single complex number, and pull back by this map to the z-plane. The z-plane is drawn to the screen, and by touching one can move the parameter and see its effect. Initially we use the simple Moebius transformation of the form z |-> (z-a)/(1-conj(a)z) which preserves the unit disc, and let a, the zero of the map, be varied by the user.