There are two special points in this image and you can probably guess which points I'm referring to. There's the one at the bottom left where this whole "Buddhajulia" seems to be growing out of. Then there's the bright one on the right which seems a rather sudden end-point for an effectively infinite chain of colorful petals. They are both solutions to the question "which z₀ maximizes the stability of the orbit for a given c?" and can be seen at work in a rather different context in another image of mine.

This image is generated by drawing two very tiny circles at these two points – w₊ and w₋ – and then running the Mandelbrot function as usual as if we were drawing a Buddhabrot. After only a handful of iterations the points growing out from the w₊ point (bottom left) have grown to cover the whole screen while the points starting around w₋ (right) have barely moved. In fact it will take several tens of thousands of iterations before the points finally splay out into a tightly coiled fractal spiral which kind of rotates around the central point. As some of the features in the image suggest the c used to generate this image lies near a period-5 bulb.