Thought Toys · Exhibit 01

Phantom traffic jams

No crash. No bottleneck. No bad driver. Just a loop of cars, each following one simple rule — and a traffic jam appears out of nothing and crawls backward forever. Slow the drivers down to summon it; speed them up to dissolve it.

0.00Avg speed
Flow
position around the loop →time ↓
stopped crawling free flow
sluggish · jamsalert · smooth
lightheavy

What you're seeing

Every car obeys a single instruction: ease onto the gas when the gap ahead opens up, ease off when it closes. That's the whole brain of every driver here — no phones, no rubbernecking, no merging trucks.

Yet when their reactions are a touch too slow, a tiny wobble doesn't smooth out — it amplifies. One driver brakes a hair too hard, the next brakes harder, and a wall of stopped cars assembles itself and rolls backward through the traffic while every car keeps trying to go forward. The cars flow through the jam; the jam never leaves. Nudge "reaction speed" to the right and watch the same crowd suddenly glide. The space-time strip records the history: those backward-leaning red stripes are the ghosts.

This is why a highway can stop dead and then, a mile later, open up with nothing to show for it. The jam had no cause. It was just traffic being traffic.

The rule, exactly. Each car steers toward a desired speed set only by its gap b: V(b) = tanh(b−2) + tanh(2), accelerating toward it at a rate you control with the reaction slider. Below a critical reaction speed the uniform flow becomes unstable and stop-and-go waves emerge on their own. (The Bando "optimal velocity" model, 1995.)

Thought Toys — a cabinet of explorable explanations. Exhibit 01.