A lighthouse beam in a von Koch snowflake fractal

Like the video this simulation shows a mathematical billiard in 6 different levels of approximation of a von Koch snowflake fractal: Level 0: 0:00 Level 1: 1:00 Level 2: 2:00 Level 3: 3:00 Level 4: 4:00 Level 5: 5:00 For each level, a light beam starts from the center, with a slowly changing angle. Whenever it reaches the boundary of the approximate fractal, it is reflected as on a perfect mirror, the color of the beam changes slightly, and its luminosity decreases. In total, 36 reflections are shown for each starting angle. To avoid numerical problems, the corners have been replaced by very small absorbing circles. The jumps in the trajectory occur whenever it encounters a corner where the boundary is concave. As the level increases, the behavior of the trajectory becomes more and more erratic, suggesting that there is no well-defined limit for the billiard dynamics as one approaches the limit of a genuine fractal boundary. After making this simulation, I found that this questio