After watching a lecture on Spontaneous Rhythms in Nature and Technology, for Physics extra credit, I couldn't stop trying to find examples around me.

The weekend of graduation in May 2026, I was at a friend's cabin in Rabun Gap, GA, and at night there were fireflies everywhere. I started thinking about how they could synchronize in a few simple rules...

The simulation on the left is a simple example of fireflies synchronizing their flashes. The rules are as follows:
 
Rule 1: at t = 0, each firefly is randomly assigned a time to wait until it flashes

Rule 2a: If a firefly "sees" another flash (a flash occurs within a 3 foot radius of it), it will abort its internal timer and flash after a short delay.

Rule 2b: The firefly will aslo start a new internal clock immediately after seeing a flash:
wait_time = t_flash - t_0 OR 
wait_time = t_flash - t_previous_flash