Octagonal representation of a genus 2 surface скачать в хорошем качестве

Octagonal representation of a genus 2 surface

Here is another little mind twister, showing 20,000 particles moving on a genus 2 surface, that is, the surface of a donut with 2 holes. The color of each particle depends on its direction, which does not change during the whole simulation. The surface is obtained by gluing together opposite sides of a regular octagon, as is beautifully illustrated in the video    • From an octagon to a genus 2 surface - Mat...   by Jos Leys (though in that video, it is not opposite sides that are identified). All 8 corners of the octagon are identified in the process, making a total angle of 8*135° = 1080° or 6 pi radians. It is thus the same type of conical singularity as in the videos    • Expanding perfect wave front on a genus 2 ...   and    • A "billiard" with a 1080 degrees angle  , though the two motions are not isometric. Music: "Night Snow" by Asher Fulero‪@AsherFulero‬ Current version of the C code used to make these animations: https://github.com/nilsberglund-orlea... https://www.idpoisson.fr/berglund/sof... Some outreach articles on mathematics: https://images.math.cnrs.fr/_Berglund... (in French, some with a Spanish translation)