Zoom in on those structures and see what happens when you get closer to them. If the patterns change as you zoom in, then this is definitely just normal sampling aliasing. The fact that you only calculate a distance and transforms it into some color means that the pattern should just be circular rings around a center point, but circular patterns with too high frequency for the display produces those particular patterns. Nothing fractal at all about it.
I cannot agree this is not a fractal, iMO this is a well defined fractal.
I think this coloring is stable, it is you probably can paint a real wooden
ball this way - this is probably effect of colouring some geometrical surface based on distance to point with cyclic palette - you will get stripes here, if distance would be counted from only one point you will
probbly get centric circles on a ball, but this distance is counted not
from one point but from each screen pixel so it results in such strange fractal (this is what i think i am not sure)
zooming the ball I think will not change the effects with covering spray
(just zooming it) but probably with rising the spatial frequenzy of palette wil uncover infinite complexity of the rings... that i suspect