A study in diffusion

Drunkard Hundreds of stumblers leave one lamppost, each step an honest coin-flip. No one steers the crowd — yet it spreads as √t and draws a bell.

Follow one walker and you learn nothing — walker #00 reels blocks from home. Average all of them and the mean sits dead on the lamp. The crowd still widens like clockwork: double the time, and the spread grows by √2.