This is a variant of the simulation https://youtu.be/b4hIUFSyjnY with a different initial configuration, which should allow for a fairer comparison: instead of being shot from a single point in different directions, 1000 particles start in the same direction, with slightly different initial positions. Each particle makes elastic reflections on the circles, as would a ray of light on a perfect mirror. The arrangements of circles are as follows:
Square grid: 0:00
Triangular grid: 1:05
"Golden mean" grid: 2:10
"Golden spiral" grid: 3:14
Randomized square grid: 4:19
Poisson process: 5:24
Poisson disc sampling: 6:29
"Golden mean" stands for obstacles shifted a constant distance to the right, and a distance proportional to phi - 1 = 1/phi = 0.618... upwards, wrapping the result from top to bottom.
"Golden spiral" means a similar construction in polar coordinates, and is found for instance in sunflowers or pineapples, see https://youtu.be/sj8Sg8qnjOg
In the Poisson process, locations are selected independently, uniformly at random.
For Poisson disc sampling, see https://bl.ocks.org/mbostock/dbb02448b0f93e4c82c3
The numbers at the bottom indicate the number of particles with x-coordinate at the left, between and at the right of the circles. At the top right the number of collisions is shown.
Table of results:
Arrangement left middle right collisions
Square grid: 1:03 906 9 85 9000
Triangular grid: 2:08 895 8 97 7761 least collisions
"Golden mean" grid: 3:12 899 3 98 9954 least in middle
"Golden spiral" grid: 4:17 907 9 84 12470 most collisions
Randomized square grid: 5:22 931 10 59 9051 most reflected
Poisson process: 6:27 876 8 117 8513 most transmitted
Poisson disc sampling: 7:32 904 7 89 9826
Render time: 8 minutes
Music: "My Train's A Comin'" by the Unicorn Heads@Unicorn Heads
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)
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