Sometimes when I want to stretch a 4x3 image to 5x3, I'll copy a couple hundred pixel vertical strip off each side, do a mirror image, then paste onto the side of the original. When I do this, I see patterns at the join points that look similar to the images here. in those cases of course, additional work is needed to remove the pattern effects. So I don't know whether the symmetries of the copy-and-paste patterns have anything to do with the topography of fractals, but patterning issues vis-a-vis the apparent randomness in a natural scene are things that take up lots of time when editing digital photos.