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.
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.
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?
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.
Testing
…
works for me. Can edit and delete.
I suspect there may be some fractal structure. This needs research. I will describe the details.