I first got Ultrafracal in 2010, and at that time I implemented some formulae for showing cubic and higher-degree Juia and Mandelbrot sets. I also formulated the so-called cubic Rudy set, which is, in my opinion, the best cubic analog to the quadratic Mandelbrot set. Like the Mandelbrot set, the Rudy set is in some sense an encyclopedia of the relevant class of Julia sets. It's all explained on my blog post http://tinyurl.com/rudyfractals
And if you're eager to start on the fractals, note that I uploaded formula and parameter files to use with Ultrafractal 5 and above. My two public files are text files rvr.ufm and rvr.upr, which you can download with Ultrafractal from the Public Formulas . And you can browse the rvr.ufm online here http://formulas.ultrafractal.com/cgi/formuladb?view;file=rvr.ufm;type=.txt.
The rvr.ufm file is a “formula” file that has the algorithms for the Cubic Julia, Cubic Mandelbrot, and Rudy sets written out as a text file in something like source code, along with a lot of comments explaining the process. The rvr.upr file gives the particular parameter settings used for certain especially attractive images.
Rudy Rucker http://tinyurl.com/rudyfractals