The Analemma is the figure created by capturing the position of the sun on a fixed time of the day (more exactly the same mean solar time) for every day of a year - analogous to a stroboscopic video of the position of the sun in the sky where the stroboscope flashes once a day at that fixed time of day.
In the above image, the position of the sun at noon (without daylight savings time) is shown for all days of 2022 for the latitude of Switzerland. The blue area represents the sky as it would be seen through a 360°-fisheye lens, with downward being South, fitting that in the northern hemisphere the sun stands in the south around noon.
The figure 8 arises as the axis of rotation of the earth is tilted compared to the plane of the orbit of the earth, as well the orbit of the earth around the sun is an ellipse rather than a circle and correspondingly the speed of the earth around the sun is not constant throughout the year.
The next figure shows the corresponding analemmas for every hour of the day (for the fixed latitude of Switzerland again) - the figure 8 here will be more or less horizontal in the morning in the east and in the evening in the west - creating a nice sort of ‘necklace’
The video shows this effect possibly more clearly by having the time of the day vary with the time of the video - the figure 8 runs along the ‘necklace’ depicted in the previous image.
In the next image, the time of day stays fixed (at noon), but multiple points of observation at different latitudes (90°N, 45°N 0°, 45°S, 90°S) are shown. The fact that at the poles (90°N/S) only part of the figure 8 is above the horizon corresponds to the fact that there are many months in the year where the sun is never raising (and others where it is never setting) during a day.
The same is shown in the video, where the latitude of the point of observation varies over time (90°N to 90°S)
In this next video the analemma is shown for different times of day (every hour) while over time the latitude of the point of observation is changing, basically capturing the above mentioned necklace for all different latitudes. At the poles, corresponding to the start and end of the video, a part of the analemma is visible for every hour - i.e., in the months when the sun never sets during the day.
The underlying calculations of the sun position have been done using the nice and concise code given by
Python Sun Position for Solar Energy and Research | by John Clark Craig | Level Up Coding
(after conversion to Kotlin).