Research on fractal structure of generalized J set utilized compound complex map

Wang Chun-mei, Hu Chun-hua

This paper generalizes Entwistle’s complex map as , constructs a set of generalized Julia sets(J sets) by using the escape time. Adopting the experimental mathematics method of combining the analytic function with computer aided drawing, this paper researches on the structure topological inflexibility and the discontinuity evolution law of the generalized J sets. The researches as below: ①generalized J sets have fold rotation symmetry and its center is the origin when  is integer;②the different choices of angle lead to the different evolution of generalized J sets.