Related to Decomposition are the "biomorphs" invented by Clifford Pickover, and discussed by A. K. Dewdney in the July 1989 "Scientific American", page 110. These are so-named because this coloring scheme makes many fractals look like one-celled animals. The idea is simple. The escape-time algorithm terminates an iterating formula when the size of the orbit value exceeds a predetermined bailout value. Normally the pixel corresponding to that orbit is colored according to the iteration when bailout happened. To create biomorphs, this is modified so that if EITHER the real OR the imaginary component is LESS than the bailout, then the pixel is set to the "biomorph" color. The effect is a bit better with higher bailout values: the bailout is automatically set to 100 when this option is in effect. You can try other values with the "bailout=" option.
The biomorph option is turned on via the "biomorph=nnn" command-line option (where "nnn" is the color to use on the affected pixels). When toggling to Julia sets, the default corners are three times bigger than normal to allow seeing the biomorph appendages. Does not work with all types - in particular it fails with any of the mandelsine family. However, if you are stuck with monochrome graphics, try it - works great in two-color modes. Try it with the marksmandel and marksjulia types.