Why Buses Always Come in Threes

Start with four buses, perfectly spaced. Watch what happens — with no interference, and with one small delay.

Natural State
No delay. No intervention.
Just buses and passengers.
0.00
evenbunched
One Small Delay
Bus 0 hits a stuck door.
45 extra seconds. That's all.
0.00
evenbunched
Headway Control
Same delay. Buses watch the gap
and adjust speed accordingly.
0.00
evenbunched
0:00
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The Pattern
A delayed bus falls behind. More passengers accumulate at stops ahead of it — they've been waiting longer. So it takes longer to board them. It falls further behind. The bus behind it catches up.

The delay compounds itself.
🌀
The Attractor
Physicists call this an attractor basin — a state the system gravitates toward. Even spacing is unstable. Bunching is stable. The simulation shows buses bunch from noise alone, with no deliberate delay, within ten minutes.
⚖️
The Fix
Headway control asks buses to watch the gap ahead and adjust speed — slow down when too close, speed up when too far. This doesn't eliminate bunching. It reshapes which state is stable. Even spacing becomes recoverable.