Comparison between 7 non-random and randomized pinballs
Channel: Nils Berglund
Date: 24/08/2021

This improved version of the simulation https://youtu.be/kiizwJYtnV4 shows 500 particles shot at various arrangements of obstacles: 
Square grid: 0:00
Triangular grid: 0:53
"Golden mean" grid: 1:46 
"Golden spiral" grid: 2:39
Randomized square grid: 3:31
Poisson process: 4:24
Poisson disc sampling: 5:16
"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
As observed by several commenters, the outcome depends much on the first obstacles hit. I tried to avoid aiming at free paths between obstacles. However, in some cases more particles are reflected back directly after the first collision, and changing the angle may change the outcome. The number of collisions counter gives you an idea of how good the structure is at keeping particles for a long time. 

Table of results:
Arrangement                                  left    middle    right    collisions
Square grid: 0:52                           389          22         89          8223
Triangular grid: 1:45                      441          14         45          5421
"Golden mean" grid: 2:38              483            2         15          3339          
"Golden spiral" grid: 3:30              468            6         26          7218
Randomized square grid: 4:23     425          13         62          7195
Poisson process: 5:15                   457            1         42          4242
Poisson disc sampling: 6:09         462            3         35          5373

Music: "Asleep with the Sun" by Unicorn Heads@UnicornHeads

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)