For more information on the principles behind these pictures, see the article on the cost of object orientation, which takes as its example fractals based on Newton's method.
All of the fractal images below are plotted within the range (-2 - 1.5i) to (2 + 1.5i).
x6 - 4 = 0
x6 + 0.5x3 - 4 = 0
x6 + 2x3 - 4 = 0
0.5x6 + 2x3 + 4 = 0