Here is the deal:
There are two interlinked circles, like in a chain. You move around one of the circles for half of eternity almost without any change. Almost. Because one day you reach a threshold, there is an action potential, a quantum jump. And you move to the second circle, where you will continue for the second half of eternity.

This is the archetype, the essence, the kernel, of the Dzhanibekov effect that my series of posts is about.

The essential math is summarized in my previous post. Here comes the animation.

Click on the image to open gif animation. It will take time to load as it is 2.5 MB.

The upper image shows the unit quaternion representing the rigid body rotation. It moves first on one circle, then makes the jump to the second circle.
The lower image shows the rotating rigid body. Time on both images is synchronized. The quantum jump is the flip of the rotating rigid body.