Three seams in a twelve-second loop

The animation is a long exposure. A bead orbits the ellipse inside the Mru mark, the ellipse precesses, and the path persists on a plate that dims each frame. Twelve seconds, drawn with ImageMagick. It was meant to loop, and it visibly restarted.

The first seam was the plate building from empty and getting wiped at the end, so the loop had a full state and an empty one. Dropping the wipe and running the bead for 540 frames before recording fixes that: the decay is exponential and the path is periodic, so the plate settles into a state that repeats. Which uncovered the second. Precession was 540 degrees, chosen because a half turn maps an ellipse onto itself, and the outline does match at the wrap. The bead does not. Half a turn lands it on the far side of the same ellipse.

Then the brief changed to starting and ending on a bare mark, which puts the empty state back and makes the changeover the problem. Frames whose mean brightness sat at the floor came to eight, four tenths of a second. Shortening the fade window only scaled that down proportionally, which was the clue.

A smoothstep leaves with zero velocity. Below roughly six percent alpha a hairline is not visible at all, so a smoothstep spends the last sixth of its window fading something already gone, and that sixth is the dead air. (1 - x) ** 0.8 declines almost evenly, arrives with real velocity, and sits under the floor for only the final three percent.

One more, which is not a seam. The ramp that eases the pen down at the start has to span more than one lap, or the taper finishes inside a single arc and reads as a stray hair rather than a line fading out.

Root mean square difference across the wrap is 0.046, against 0.065 for an ordinary frame advance. The loop point is a smaller change than a normal step.