Based on the equation of su ( 2 ) algebra dynamic , the chaos problem is discussed in the linear su ( 2 ) nonautonomous quantum system . and a very important and interesting result is found that the complementary chaos phenomenon exists in the system . besides , the box dimension of fractal graph is calculated 利用su ( 2 )代数动力学方程讨论了su ( 2 )线性非自治量子系统中的混沌问题，并且发现了一个非常重要而有趣的结果： su ( 2 )线性非自治量子系统中存在着互补混沌，同时计算了分形图形的记盒维数。
This paper is devoted to seeking formulas and rules of representation for generating new fractal graphics . the main works are as followed : ( l ) construct new formulas for new fractal aspects after revisited methods for the visualisation of mandelbrot and julia sets based on ifs , we described the other new formulas originating from z z2 + c . including norton and polynomials iterated function , which have integer index instead quadratic index , we also constructed formulas with complex number index . 3 - d dynamical system is discussed then . besides the most widely used sequential visualisation methods , we designed two methods to change the original vectors and get new graphics with special effects 在对公式指数的推广中，包括指数为整数的牛顿迭代法和多项式迭代法，还包括指数为复数的迭代公式；在离散动力系统的吸引子生成算法讨论中，将复数z向高维空间推广，重点论述了生成了三维离散动力系统吸引子的收敛条件，实现了此吸引子对应的三维空间向量在平面上的投影图的条件；还讨论了迭代前对初值点进行两种不同变换对得到的分形图形的影响，以及这两种变换组合图形的生成。
In virtue of the knowledge related to fractal theory , all fractals algorithms in the paper have already been realized on computer , such as mandelbrot sets , julia sets , l system and iterated function system , etc . and their fractal figures have been drawn . meanwhile , to obtain a better visual effect and simulate actual natural scene , software adopts the real color and color palette to enrich figures , and color animated cartoon to change them . to show the self - similarity and infinitive tractility of fractal figures , partial zoom has been made on them 本文运用分形理论实现多种分形算法，在计算机上生成mandelbrot集， julia集， l系统， ifs迭代函数系统等典型的分形图形，同时运用真彩色及调色板技术丰富图形的色彩，实现了色彩动画，使其更真实的模拟自然景物；运用鼠标编程技术实现对图形局部的放大和缩小，体现分形图形的自相似性和无限延展性；提供多组参数，利用分形图形的混沌特性，通过微小的参数变化，生成完全不同的分形图形。
