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.
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.