Cellular automaton for highway traffic with spontaneous jam formation
The Nagel-Schreckenberg model (1992) is a probabilistic cellular automaton with 4 rules: accelerate (v→v+1), brake to gap (v→min(v,gap)), randomize (v→v-1 with prob p), and move. Despite simplicity, it reproduces phantom traffic jams, capacity drop, and the fundamental diagram — a phase transition between free-flow and congested phases.