Look at the image above. You should notice bands of colors. As discussed before, the colored pixels are not actually part of the Mandelbrot set, but points that are outside of the set, and they are colored based upon how long it takes for us to declare that a point has “escaped.”
The problem with such an algorithm for assigning color is that it creates bands of color, which are clearly visible in the image above. While these bands have some meaning, they are an annoying visual artifact. If the goal is the create pretty pictures, it would be nice if we could get rid of those bands.
The good news is, it is possible. Roll your mouse over the above image, and have a look. The image that is displayed on rollover is identical to the original, but colored using a smooth coloring algorithm.
The bad news is that I am finishing up finals grading, and don’t have much time to go into it right now. Also, I am already a day late getting this up. I promise a more complete explanation in the days to come.