Midnight Crowd: Pedestrian Wave Dynamics (3D)

Crowd

Crowd density 160

Desired walking speed 1.30 m/s

Repulsion strength A 2.10

Repulsion range B 0.55 m

Bidirectional ratio 50 / 50

Click the plaza floor to drop a lamppost the crowd must flow around. Drag to orbit, scroll to zoom.

Live Readouts

Mean speed

0.00 m/s

Peak density

0.0/m²

Flow state

Smooth

Agents

The real physics

Agents circle a closed plaza avenue around the countdown tower — a ring topology chosen so the crowd has no start or end, only density. Each agent relaxes toward a desired tangential speed while an anisotropic, front-weighted exponential force keeps it clear of neighbours and lampposts (Helbing & Molnár's social-force model — an agent reacts more strongly to who is ahead of it than behind, exactly like a real pedestrian):

dv/dt = (v0·ê_t − v)/τ + Σⱼ w(φᵢⱼ)·A·exp((rᵢⱼ−dᵢⱼ)/B)·n̂ᵢⱼ
w(φ) = λ + (1−λ)·(1+cosφ)/2

No agent is scripted into a lane. At low density the two flows interpenetrate freely; past a critical density the front-weighted repulsion makes counter-flowing streams spontaneously separate into lanes, and — pushed further — local compressions can't dissipate fast enough and a stop-and-go density wave rolls backward around the ring, visible in the scrolling angle-vs-time strip below the plaza.

Clockwise flow Counter-clockwise flow

angle around plaza → · time ↓ (density wave)

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