Expanding perfect wave front on a genus 2 surface скачать в хорошем качестве

Expanding perfect wave front on a genus 2 surface

This is the geometric optics version of the wave simulation in    • Waves around a conical singularity   - a version with a different initial configuration is shown in the video    • A "billiard" with a 1080 degrees angle   Here 50,000 particles start from the same point, but in all directions. The rainbow color scheme indicates the direction of a particle, which remains the same during the whole simulation. Opposite sides of the L-shaped domain are glued together, so that particles leaving through one side come back from the opposite side. If the same procedure were used with a rectangle, the resulting geometry would be that of a torus, or surface of a donut. In this case, we get a surface of genus 2, that is, a donut with two holes. All angles of the L shape meet at a single point of the surface, as do the middle points of the long sides. The total angle at this so-called conical singularity is therefore 1080° (270° at the inner corner, plus 5 times 90°, plus twice 180°), or 6 pi radians. Music: "Inkling", by Slenderbeats‪@slenderbodies‬ 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)