3 light sources in a Penrose unilluminable room
Channel: Nils Berglund
Date: 29/09/2021

Like the video https://youtu.be/iInarJloEzs this simulation shows particles in a Penrose unilluminable room, this time with particles starting in all directions from 3 different starting points. 
The illumination problem asks the following question: assume you have a room with mirrored walls. Is it always possible to place a light source in such a way that no dark corners remain in the room? Of course, the room has to be "in one piece" (connected, as we say in mathematics): it should not consist of several separate rooms. 
The problem was formulated by Ernst Straus in the 1950s, and first solved by Roger Penrose in 1958. He constructed a room that cannot be illuminated completely, wherever you put the light source. The room is constructed with two half-ellipses connected by straight parts, in the middle of which one puts two mushroom-shaped protuberances. The rounded parts of the mushrooms are also half-ellipses, whose vertices are placed at the focal points of the large half-ellipses.
The simulation shows 20 000 particles starting in all directions from three different points. The color of the particles is different for each starting point, and does not change in the course of the simulation. The particles move in straight lines, until they encounter a wall, on which they bounce in the same way a ray of light is reflected on a mirror. For each color, there is part of the room that cannot be reached by particles of that color. YT compression is not very kind to the color red, it seems, sorry for that...

Render time: 4 minutes 30 seconds

Music: "Canal 3" by Quincas Moreira@QuincasMoreira

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)