M-J Chaotic-Fractal Image Spectrum - The Crystal of the Science and Arts

摘要

Chaos is the fourth greatest discovery of 20th century after relativity, quantum theory and DNA and will be one of the hottest research topics of 21th century. The visualization and analyzing of chaos-fractal system by computer forms a new research field — the study of M-J chaotic-fractal images to explore nature appearance and inner relationship of the world. In this paper, the background and current development of this filed was introduced. The principles and methods used for constructing chaos-fractal systems were analyzed. Some of the representative M-J chaos-fractal images constructed by correspondence theories were figured out and the inner structure and rules of the images obtained by huge amounts of computer mathematics experiments were given. The achievements of theories and its applications of this field made by the author and his group in recent years were also discussed.