The glowing stack emits a plume of an airborne carcinogen (think benzene, formaldehyde or a PAH mixture — IARC Group 1–2B substances). Its spread follows a simplified Gaussian plume model: concentration falls off with crosswind distance and widens downwind, scaled by the emission rate and inversely by wind speed — a stronger wind dilutes the plume faster but also drags it further before it disperses. Each glowing dot is a person scattered around the site at a fixed location; the local concentration they experience accumulates into a lifetime dose, and dose converts to cancer risk through a linear no-threshold model — the same assumption regulators use for genotoxic carcinogens, where no exposure level is treated as fully "safe", only progressively lower-risk. Meanwhile the body's own detoxification enzymes and DNA-repair machinery continuously clear a fraction of the accumulated dose, so risk growth is a tug-of-war between ongoing exposure and repair.
C(x,y) = Q / (2π·σy(x)·u) · exp(−y² / (2σy(x)²))
dose/dt = C(x,y) − repair·dose
risk = 1 − exp(−k·dose) (linear no-threshold)
- Emission rate (Q) — how much carcinogen the source releases per unit time; scales the whole plume up or down.
- Wind speed (u) — higher wind dilutes concentration near the source but carries the plume further downwind before it fades.
- Population size — how many people around the site are being tracked; more points make the downwind risk gradient easier to read.
- Detox / DNA-repair rate — how quickly the body clears accumulated dose; this is what keeps low-level chronic exposure from being as dangerous as an equivalent acute dose.
- Time acceleration — compresses years of chronic exposure into seconds so long-latency effects become visible.
Real-world relevance: this is why environmental health regulation cares about exposure duration and distance from a source at least as much as peak concentration, and why reducing emissions at the stack (source control) helps everyone downwind at once, while relying only on individual detox capacity does not.