Actually, the majority of these images are not fractals, but represent the first step(s) of an iterative construction that would ultimately produce a fractal (or total chaos...)
The method used is essentially that of selecting a complex function f(z) and then repeatedly applying it to a starting point corresponding to each pixel. A bound is applied on the number of iterations or on the value reached. Then a color is selected depending on the number of iterations performed before convergence, divergence, or on the last computed value. Sometimes a secondary function is applyed before selecting colors.
Unfortunately, I've lost trace of the function I used for several of these images, so I can't recreate them with better resolution than the current 1920 × 1080. Apart from applying a watermark with imagemagick, images have not been edited.