Artistic Fractal Images for Complex Mapping F(z) and T(z)

The generalized 3x+1 function T(z) can generate fractal images. So a complex mapping F(z) is constructed based on T(z), and visualized it using escape time algorithm. Because the images of T(z) and F(z) are intricate and rich with certain artistic value, several methods are proposed to generate pseudo-3D artistic fractal images. The methods are all based on escape time algorithm and color map, which use the distance divided approach to draw non escape areas and the orbit trap to draw the escape areas. The experiments show that these methods have better effect, are fast and easy to implement.