中文摘要：

提出了3x＋1的又一推广函数F（z），指出其能引出复杂的分形结构．分析了函数F（z）的基本数学特征，探讨了该映射在C平面上广义M集的图像特征，并绘制了其广义M集的部分美妙的分形图像．利用调色板技术和轨迹井技术结合的方法，绘制F（z）广义M集的艺术分形图像，同时在Carlson（Carlson Paul W．Two artistic orbit trap rending methods for Newton M—set fractals[J]．Computers＆Graphics，1999，23（6）：925—931）的基础上提出了环状M集轨迹井，取得了良好的艺术效果，给人一种美的享受．

英文摘要：

We put forward another generalized 3x ＋ 1 function F（z）, and pointed out that the function can produce the complicated fractal structure. In the meanwhile, we analyzed the basic mathematical features of the function F（z）, studied the images features of the generalized M-set in the C-plane, drew the some beautiful fractal images of the generalized M-set. The artistic fractal images of the generalized M-set were drew by using of the colormap and the orbit trap technology in the paper. And according to the orbit trap of the tangent circle which is put forward by Carlson （Carlson Paul W. Two artistic orbit trap rending methods for Newton M-set fractals [J]. Computers ＆ Graphics, 1999, 23（6）： 925-931）, we put forward the orbit trap of the circle M-set. This new orbit trap obtains good artistic effect. It gives people wonderful enjoyment.