Tools are needed to visualize, understand and then extract useful information in complex continuous dynamical systems including ocean flows, hurricane structures, flight path, gravity waves and some bio-inspired fluid flows. A lot of work in dynamical systems focuses on understanding different types of behaviors in a model, such as elliptical zones, hyperbolic trajectories, chaotic attractors, mixing regions, Poincare section, bifurcation diagram and finite time Lyapunov exponent. The aim of this project is to develop computationally efficient numerical algorithms for one or some of these visualizing tools.