Varied cycles of the dynamic system constructed of DCT basis function and image

The results of the existing literature reveals that the dynamic system is in vast probability of chaos by using the sine function as an auxiliary function. Studies have shown that DCT with magnification owns stronger chaotic structure abilities than any other ones. Relocating matrix of DTC basis function as auxiliary function, which forms the dynamic system with gray image matrix has characteristics in initial value sensitive, multicycle, complexity of bifurcation phenomenon, positive of approximate Lyapunov exponent and so on. There is found to be similar chaotic attractors, whose shapes and contours are similar to the face image of the same person. These attractors used in image recognition, video retrieval and other fields have advantages like simple algorithm, short recognition time and good recognition effect. It is an admirable example of studying chaos in finite field, we ought to study the mechanism of the chaos and other applications in the fields of data processing as a consequence.