This thesis develops the concept of the Chaotic Transient Computation Machine (CTCM) where the mixing of trajectories creates "hot spots" that are characteristic to a particular input class. These hot spots emerge as input patterns are fed into the chaotic attractor. This scheme allows an observer neuron that is trained on these hot spots is able to classify patterns that would otherwise unclassifiable by such a simple neural setup (i.e. a nonlinearly separable problem space). This thesis also demonstrates that CTCM is applicable to a variety of chaotic attractors and thus the concept is generailizable to any chaotic attractor.