基于区域赋色法的复分形图生成研究
Research on Complex Fractal Graph Generation Based on Region Coloring Method

用逃逸时间算法绘制二维复平面上的广义分形集时，常用的着色方案主要有双色法、基于迭代次数的层次赋色法、基于距离的赋色法等颜色方案。前面几种着色方案非逃逸区颜色单一，逃逸区颜色过渡明显。基于逃逸时间算法本文提出了一种新的区域赋色法，针对广义Julia集和Mandelbrot集，用不同色图矩阵分别对逃逸区和非逃逸区像素点进行着色，该方法基于MATLAB软件实现简单，可以同时渲染广义分形集的内外结构，且颜色过渡平缓。
When the escape time algorithm is used to draw the generalized fractal set on the two-dimensional complex plane, the commonly used coloring schemes mainly include two-color method, hierarchical coloring method based on the number of iterations, and distance-based coloring method. In the preceding schemes, the color of the non-escape zone is single, and the color transition of the escape zone is obvious. Based on escape time algorithm, a new region coloring method is proposed in this paper. For generalized Julia set and Mandelbrot set, different color matrix is used to color the pixels in the escape region and non-escape region respectively. This method is simple to realize based on MATLAB software, and can simultaneously render the internal and external structure of generalized fractal set with smooth color transition.