Seems to me that the images on Bourke's site _are_ produced using the general "Buddhabrot" technique (splatting points onto an image). Although each image appears to only represent a single orbit sequence and the reject condition is inverted so that only stable orbits are shown.
I've personally found the technique very versatile and have had a lot of fun playing around with it and exploring different variations. Was excited enough about the whole thing that I created a website for sharing some of my explorations: https://www.fractal4d.net/ (shameless self-advertisement)
With the exception of some Mandelbrot-style images all the rest are produced by splatting complex-valued orbit points onto an image in one way or another.
Had to make an account just to say thank you for posting the working link. The diffraction pattern instantly reminded me of a (continued fraction) fractal I found a while ago: https://www.fractal4d.net/work/vitruvius/
Somewhat related to the Mandelbrot fractal its iterated formula is f(z) = -z^-1+c = c-1/z
I've personally found the technique very versatile and have had a lot of fun playing around with it and exploring different variations. Was excited enough about the whole thing that I created a website for sharing some of my explorations: https://www.fractal4d.net/ (shameless self-advertisement)
With the exception of some Mandelbrot-style images all the rest are produced by splatting complex-valued orbit points onto an image in one way or another.