More chaos in a 5-petaled elliptical flower billiard
Channel: Nils Berglund
Date: 2021-06-11

Simulation of 30 000 particles in an elliptical flower billiard. These billiards have been introduced by Leonid Bunimovich to provide examples of systems that can be proved to have mixed dynamics, with both regular and chaotic trajectories, see https://arxiv.org/abs/2105.06333 
This particular example is constructed by starting with a regular pentagon. The boundary of the billiard is formed by elliptical arcs, which meet at the mediators of the pentagon's sides (particles do not interact with the the gray lines, which just illustrate the construction of the boundary). Each elliptical arc has two non-consecutive vertices of the pentagon as focal points. The parameters of the ellipse have been chosen to make the boundary more different from a circle than in previous simulations. The trajectories can be divided into "tracks", which turn around the pentagon without touching it, and a "core", made of trajectories that always cross the pentagon's sides. Colors have been chosen to help distinguishing between both types of trajectories.

Music: "Amazement", by Freedom Trail Studio@FreedomTrailStudio

Current version of the C code used to make these animations: https://github.com/nilsberglund-orleans/YouTube-simulations
https://www.idpoisson.fr/berglund/software.html

Some outreach articles on mathematics:
https://images.math.cnrs.fr/_Berglund-Nils-1343_.html
(in French, some with a Spanish translation)