Another geodesic line

Saturday. It was warm and sunny. Went for a bicycle raid. Working on generating the exceptional geodesic for d=0.5.
But, until that is ready, I have made another geodesic line on the three-sphere, this time for d=0.4999999 and 180 degrees rotation in 4D.

Click on the image to open animation

Update: I have produced the geodesic for d=1/2. Here is the result for t going from -2000 to 2000:

It is a great surprise for me. Is it really one closed line? Or, under microscope, it will split into many-many lines, very close, but with a subtle structure?

Update at 22:12
Progress. Here is one point on the trajectory (I created animation to see how it is moving)

And here is zoom on the line when this point was:

The line is not a line. These are many many lines, but very close to each other.