DrunkardHundreds 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.
Steps taken0
Spread σ = √t · ℓ0.0 paces
Walkers loose0
Mean displacement0.0 paces
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.