This research is an investigation of the practical applications of the theories of chaos towards understanding and predicting the random aspects of seismicity. If successful, these methods hold great promise for becoming a practical method of predicting earthquakes on any chaotic fault system. Utilizing earlier promising results, this work will estimate the amount of time that any deterministic model reflects the initial conditions rather than the chaotic nature of fault systems. A test will be made of two recently proposed, attractor-based methods of predicting seismicity on those fault systems. This research is a component of the National Earthquake Hazard Reduction Program.