So far, these all look like the Mandelbrot set with a few small additional features. It appears that way only because of my selection of what to keep and what to show here. Initially I was disappointed in the results. Most results were uninteresting. The wrong sequence, or the wrong choice of formula wipes out all fractal like features. I might have given up, except that I had invested too much time in writing the software.
So, baby steps. Start with the simplest formula and the simplest sequences.