Function sequence 
Six cycle of functions chosen at random from four different functions. Two affine transformations, z = z2, and z = z + c.
I think there may be a lot of potential with this scheme. However in a very quick investigation, I found that infinite random sequence and long (10 or more) cycles do not produce good results. Everything escapes quickly. Also different random seeds produce very different results. I need to investigate this with deterministic, or at least less-random, function selection.
I should point out that this is not entirely new territory. With a different coloring scheme, and without the “+c”, this starts to look like IFS and Flame fractals.