【摘要】 利用逃逸时间算法绘制M J混沌分形图谱 ,通过计算机数学实验找到Mandelbrot集的普适常数和相应充满Julia集的近似标度不变因子 ,定性说明了M J混沌分形图谱标度不变的特性 .同时 ,通过实验与数据分析发现Mandelbrot集周期芽苞的Fibonacci序列的拓扑不变性 ,找到M 集内的黄金分割点 .最后给出由Mandelbrot集参数平面上某个吸引周期芽苞中的参数与动力平面上相应Julia集图像结构之间的对应关系 ,并给出M J周期轨道的递归公式和多重结构特征图的猜想 .更多还原

【Abstract】 A series of M-J chaotic-fractal image families are generated by the escape time algorithm. Universal constant in the Mandelbrot set and approximate scaling invariable factor in the Julia sets are discovered, which qualitatively demonstrate scaling invariance of M-J chaos-fractal images. Furthermore, the topological invariance on the periodic buds Fibonacci sequence and golden section point in the Mandelbrot set are discovered. Lastly, the corresponding relation of M-J between a parameter c in an attractive periodic bud of the Mandelbrot set and image structure of the Julia sets on dynamical plane are presented, and a recursive formula on periodic orbits of M-J and characteristic images on multiple structure is given. All results show a better understanding on the structure of M-J sets.更多还原