An implementation of the cellular automaton created by John Conway.
AKA the Locker Problem, an interesting result happens when you ask N people to flip every Nth light switch. Check out Numberphile's video for more information.
Buffon's Needle is a mathematical question with a surprising solution. As it turns out, when you calculate the probability that a line segment of length N intersects a series of parallel lines spaced N units apart, pi makes a unexpected appearance. For Pi Day 2022, I used this fact in reverse to approximate the value of pi by simulating toothpicks being dropped onto evenly spaced lines.
Before modern computing, pi had to be calculated by hand. Archimedes did this by inscribing a polygon inside a unit circle and circumscribing one outside to find the lower and upper limits of what pi possibly can be. This is a visual demonstration of this method. Check out Veritasium explanation for more details.