Physics
I love setting up simulations and numerical illustrations of physics. Here are some of the simulations I made that I think are worth sharing.
Double pendulum
A single pendulum behaves completely predictably, but add another pendulum to the end of the pendulum, and the system becomes chaotic.
Vicsek flock
A simple illustration of collective behavior arising from simple local rules. Common example of a nonequilibrium phase transition.
Forest fire
Trees grow, lightning strikes, fire spreads. This simple model tunes itself to criticality, and is enchanting to watch.
Cellular automata
Again, simple rules give rise to surprisingly complex behaviors.