❄️ ❄️ Snowflakes

Ice forms a hexagonal crystal lattice — water molecules hydrogen-bond in hexagonal rings, creating a structure with six-fold rotational symmetry. The basic ice unit cell is hexagonal, so any crystal grown from water vapour inherits this symmetry. The six arms of a snowflake grow from the six corners of the hexagonal prism seed crystal.

Each arm of a snowflake experiences essentially identical conditions — temperature, humidity, and growth rate — at any given moment, because the crystal is tiny (typically 1–5 mm) and all six arms sit in the same local microenvironment. As the snowflake drifts through the cloud, changing conditions affect all arms equally and simultaneously, synchronising their growth into matching shapes.

No two snowflakes are identical in practice. The number of possible arrangements of 10^18 molecules in a snowflake's structure is so astronomically large that identical snowflakes would never be expected to form. Simple snowflakes (small hexagonal plates or columns formed in specific lab conditions) can appear nearly identical, but complex dendritic flakes grown in natural atmospheric conditions are effectively unique.

Elaborate stellar dendritic snowflakes (the classic six-armed snowflake shape) form around −15°C with high water vapour supersaturation. At warmer temperatures (0 to −3°C), thin plates form; at −3 to −8°C, needle shapes; at −8 to −12°C, hollow columns. The Nakaya morphology diagram maps all snowflake shapes to their growth conditions.

Snowflake growth is modelled using cellular automaton rules (Reiter model: each cell represents a small region that can be frozen, liquid, or vapour; growth rules propagate freezing based on neighbour states and vapour diffusion), diffusion-limited aggregation, or phase-field models solving coupled equations for ice fraction and vapour concentration. These simulations reproduce dendritic branching, plate formation, and morphological transitions matching the Nakaya diagram.