Rule 30 (1D Cellular Automaton)

Introduced by Stephen Wolfram in 1983.
A 1-dimensional array of cells evolves over time, generating a new row downwards (or upwards, like a printer). A cell's next state depends on itself and its two neighbors. The rule 00011110 (30 in binary) dictates this evolution.
Despite simple, deterministic rules, it generates complex, chaotic, and seemingly random fractal patterns (Class III behavior). It is so chaotic that the center column is famously used as a pseudorandom number generator in Mathematica.