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.

4 thoughts on “Another geodesic line

  1. Przypadek d=1/2:
    Wiazka ma skonczona grubosc, czy moze bedzie sie rozlazic na cala dostepna przestrzen?
    Jesli skonczona, to czym ta grubosc jest ograniczona?
    Jaka jest struktura wiazki – linie sa rozmieszczone rownomiernie, czy moze gdzies sie zageszczaja?

    1. I have installed a different plugin for test. In theory it should allow registered users to edit their comment without time limit, and also delete. It needs testing.

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