Generalized M-Set Produced by Generalized 3x+1 Function and the Artistic Fractal Images

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 fractalsJ.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.