Indexing the archive…
Your Universe of Digital Possibilities
In 2008, Yuki Sugiyama put 22 cars on a single-lane circular track and told the drivers one thing: hold a steady speed, keep the gap. For a few seconds the ring flowed. Then — no accident, no obstacle, no merge — a knot of brake lights appeared out of nowhere and began to crawl backward around the loop, against the traffic, swallowing car after car. The phantom jam the cellular automaton predicted had walked straight off the screen and onto a real road.
Each car, each tick: speed up by one, but never faster than the gap g ahead or the limit vmax; then with probability p tap the brake for no reason; then move. That one random tap is the whole story — set p = 0 and traffic never jams on its own.
Flow (cars per minute past a point) is density times speed. As density ρ climbs, flow rises to a peak at the critical density ρc, then falls back to zero in gridlock — the inverted-U every road obeys, and the proof that more cars can mean less throughput.
Cars are conserved, so density flows like a fluid — and where fast, sparse traffic meets a dense pack the solution forms a shock: the sharp upstream edge of a jam, a discontinuity that drifts backward through the cars at a speed set by the diagram, not by the drivers.
The Jam ties three views of one road together: Greenshields’ measured inverted-U, the LWR conservation law that makes a jam a backward-travelling shock, and the four-rule NaSch automaton that breeds that shock from nothing but a random brake-tap. The jam wave is a density soliton— a self-sustaining lump that, like The Soliton, holds its shape as it moves — except here it carries The Sandpile’s self-organized stop-and-go: each braking car topples the one behind it. And the free-flow → jam onset is a genuine phase transition, the same critical threshold as The Threshold, where below it a fluctuation heals and above it the same fluctuation runs away.