John Conway's Game of Life is a classic cellular automaton simulation with cells on a grid that live or die based on the properties of their neighbors. Academics and nerds have long been exploring how complex systems can arise from a seemingly simple set of rules. Theoretically, anything computable can be computed inside the simulation!
I built this with JS/React in about half a week as part of the computer science curriculum at Lambda School.
Check out the deployed project here for a bit more background and to tinker with the game.