Right, that was the comment below the image. It is a catch 22 where it is easy to have a mechanism cycle one full cycle stopping where it started, but when you make a looping movie, you can always tell where that loop starts and ends. Movies conversions are not exactly frame based anyway and therefore the seam is even more notable in most cases.
If you try to run GIFs too fast, they too will have artifacts. Although I dropped the 1st image, it still has a minor random stutter. It is not consistent if you watch it carefully. You can slow down the animation and it runs flawlessly but you can see the frames. A .01 second delay in PhotoScape seems to have a bug... it ignores it. A .02 second delay is 30 fps and that is what the animation is. A .03 second delay is likely optimal from a processing point of view.