This thesis presents an investigation into the idea of using Cellular Automata to compress digital data. The approach is based on the fact that many CA configurations have a previous configuration, but only one next generation. By going backwards and finding a smaller configuration we can store that configuration and how many steps to go forward, instead of the original. In order to accomplish this an algorithm was developed that can backtrace a 2 dimensional CA configuration, listing its previous configurations. The algorithm is used to find a rule that often has previous configurations and also find an example where a matrix appears to become smaller by backtracing. The conclusion, however, is that when increasing the configuration size to trace the algorithm rapidly becomes too time consuming.