Urban Heat Island Edge Effect: Diffusion-Coupled Microclimate (2D)

This 2D companion to the 3D urban-heat-refugia simulator keeps the same land-cover thermal-inertia model — road, building and park tiles each with their own heat-storage capacity and time constant — but adds the physics the 3D sim leaves out: horizontal heat diffusion between neighboring tiles. Instead of each tile relaxing toward its own solar target in isolation, this sim solves a coupled 2D reaction-diffusion equation across the whole grid, so heat measurably bleeds from hot pavement into adjacent parks and cooling bleeds the other way — the real, documented "park cool island" edge effect that gives green space a cooling footprint larger than its own boundary. An invisible isolated (no-diffusion) copy of the same grid runs alongside the visible one purely as a baseline, letting the sim report exactly how much warmer park edges get and how much cooler pavement edges get because of mixing — a number that should shrink to zero as the mixing slider is turned down, and does. A pollinator population performs negative thermotaxis by bilinearly sampling the diffused field's gradient, accumulating heat stress above a settable tolerance limit until sustained exposure causes local die-off, exactly as in the 3D sim.