分形图案的快速生成法

Fast Algorithm for Fractal Images

该文给出了经典Ｍａｎｄｅｌｂｒｏｔ集合和Ｊｕｌｉａ集合的概念，分析了常用的点点计算法的特征，在此基础上设计出快速的有限递归细分算法（ｆｉｎｉｔｅｒｅｃｕｒｓｉｏｎｓｕｂ－ｄｅｖｉｄｅ，简称ＦＲＳ）。利用这２种算法生成Ｍａｎｄｅｌｂｒｏｔ放大集以及三角函数、指数函数、Ｇａｕｓｓ和函数、Ｎｅｗｔｏｎ解函数的Ｊｕｌｉａ集合并进行比较，ＦＲＳ法一般要比点点计算法快３～５倍，解决了微机生成分形图案时间太长的问题。通过快速算法显示出分形图案的内部蕴涵的精妙结构。

The concept and the creating method of the classic Mandelbrot set and Julia set are given in this paper. A general algorithm computing point by point is analyzed, meanwhile a fast algorithm. Finite recursion subdivision method is designed for blow up of Mandelbrot set and Julia set of angular function, exponential function, Gauss sum function, Newton method. Compared to PPC method, FRS method is 3 to 5 times faster than PPC. The problem of the unendurable running time is solved, and the intricate structure of fractal images are displayed. An effective method is provided for fractal research.