Below a threshold, nothing. Above it, everything at once.
Henri Bénard set a shallow dish of whale oil over a warm plate in 1900 and watched a grid of cells appear where there had been only still liquid. Lord Rayleigh gave it the number: below a critical Ra ≈ 1708, heat crosses the layer by conduction alone and nothing moves. Cross it, and buoyancy wins.
What emerges is not imposed from outside. The fluid selects its own wavelength — cells roughly as wide as the layer is deep — and packs them into the tightest tiling the plane allows. Warm the plate harder and the cells churn faster, break, and re-knit; the pattern is never quite finished.
Buoyancy
Fluid at the base expands, grows light, and lifts. It rises fastest through the centre of each cell — the bright plume you see climbing.
Tessellation
Rising columns must share the plane with the falling sheets between them. Hexagons pack six neighbours around each plume with the least wasted edge.
Reorganisation
No cell is permanent. Neighbours steal heat, edges migrate, plumes wander and merge — the quilt slowly reshuffles while its statistics hold.