Research on Chaos-Fractal Images Constructed by Complex Mapping z←sinz~2+c

The M-J chaos-fractal system constructed by polynomial function sets was extended to studying the generalized M set and J set, which are constructed by complex mapping z←sinz~2+c, so as to plot the chaos-fractal images of M and J sets by use of escape time algorithm. The distribution rules of main periodic buds in M set were found by lots of computer mathematic experiments and compared with the M set constructed by the typical complex mapping z←z~2+c, thus revealing the differences between them. It was found that the generalized J set constructed by complex mapping z←sinz~2+c is characterized by discontinuity. The image structure and position of periodic point were analyzed, from which a conclusion could be drawn that it has an infinitely embedded and self-similar fractal construction. The study on J set fractal image corresponding to the point in each periodic bud reached a conclusion that the number of periods of a point in a periodic bud of M set equals to that of the periodic attraction orbit of corresponding J set. The relationship between M set and J set were also discussed.