🚦 Nagel–Schreckenberg

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🚦 Nagel–Schreckenberg Model

A cellular automaton for single-lane highway traffic, introduced by Kai Nagel and Michael Schreckenberg in 1992. Despite its simplicity, it reproduces realistic phenomena: free flow, synchronized traffic, and spontaneous jam formation (stop-and-go waves).

The road is a 1D ring of cells, each either empty or occupied by one car with integer velocity v ∈ [0, v_max]. Every timestep, all cars update in parallel:

1. Accelerate — v → min(v+1, v_max)
2. Brake — if the car ahead is closer than v, slow down to gap
3. Randomize — with probability p, reduce speed by 1 (the crucial noise)
4. Move — advance v cells forward

See Wikipedia for the full story.

UI Reference

Length (L)

Number of cells on the ring.

Max speed (v_max)

Maximum velocity a car can reach.

Randomization (p)

Probability of spontaneous braking each step.

Density (ρ)

Fraction of occupied cells.

Speed

Milliseconds per step (0 = fastest possible).

Run / Pause

Start or stop continuous simulation.

Step

Advance by one timestep.

Reset

Regenerate the road with current parameters.

Road view: cars colored by speed (red = stopped, blue = v_max). Space–time diagram: time increases downward, each row shows the full road at one timestep.