Midnight Crowd: Pedestrian Wave Dynamics (2D)

Crowd

Crowd density 140

Desired walking speed 1.30 m/s

Repulsion strength A 2.10

Repulsion range B 0.55 m

Bidirectional ratio 50 / 50

Click the avenue to drop a lamppost the crowd must flow around. Drag to pan, scroll (or pinch) to zoom.

Live Readouts

Mean speed

0.00 m/s

Peak density

0.0/m²

Flow state

Smooth

Agents

The real physics

Each pedestrian is a self-driven particle in Helbing & Molnár's social-force model. Its velocity relaxes toward a desired speed and direction, while every neighbour and wall pushes it away with a force that decays exponentially with distance:

dv/dt = (v0·ê − v)/τ + Σⱼ A·exp((rᵢⱼ−dᵢⱼ)/B)·n̂ᵢⱼ + walls

No agent is told to form a lane or to slow down — lanes and stop-and-go waves are pure emergent consequences of many agents solving this same local force balance at once. Push density up and you'll see local clumps where repulsion can't clear fast enough: a compression wave that propagates backward through the crowd exactly like a phantom traffic jam, visualised below the avenue as a scrolling position-vs-time strip (brighter = denser).

t = 0.0 s

→ flow ← flow

position → · time ↓ (density wave)