The areas of nonlinear dynamics, and computation have typically been regarded as separate areas of study. This thesis explores the intersection of these disciplines. I first investigate a recent model that attempts to emulate logic with an array of threshold coupled nonlinear elements. I describe a variation on this system with which to overcome some of its inherent limitations. This correction, while successfully addressing these limitations, remains a less than satisfying computational implementation. I then consider a second system in which a single nonlinear, multivariate map is used to implement all logic gates. The logic "hardware" described by the multivariate map can be reprogrammed with "software" parameters applied to the update map. This system illustrates why logic requires nonlinearity.