This talk will introduce Fixed Point Iteration (FPI), an often overlooked and neglected iterative method. In this session FPI's bahavior will be visually illustrated and show that it compares very favourably with Newton Iteration. The talk will also cover how to apply it to a diverse range of practical problems, including rendering water using flow maps, temporal reprojection of images, and sampling the height of deep ocean waves. This session will also show the surprising equivalence of FPI to raymarching of distance fields. The talk will equip attendees with the confidence and ability to recognize problems that require some kind of search or iteration to solve, and with the skills and knowledge to apply FPI to find a solution.