COMPOSITIONAL convection occurs when a liquid containing more than one chemical component undergoes fractional crystallization. Above a critical solidification rate, a solid–liquid mixed phase (or 'mush') develops which can exhibit spatial gradients of permeability and flow due to preferential dissolution and precipitation in the upwellings and downwellings respectively. A striking, but poorly understood, example is when upflow occurs in narrow, crystal-free, cylindrical channels or 'chimneys'. Such dynamic effects may occur in the Earth's core1, crustal magma reservoirs2, hydrothermal systems at mid-ocean ridges3 and during the diagenesis of sedimentary rocks4. Using experiments designed to maximize the effects of dissolution and precipitation, we show that chimney formation can be related to a known planform of convection. Just above marginal stability, upwelling (and dissolution) occurs along the perimeters of hexagonal cells, with downwelling (and precipitation) at the centres, giving rise to a tessellated network of vertical, crystal-free channels. Subsequent focusing of the upflow at the nodes of the hexagons and recrystallization in the linear channels results in isolated chimneys at the nodal positions.