No two snowflakes are exactly alike — a statement that is essentially true, given that a single snowflake contains roughly 10^18 water molecules, and tiny differences in temperature, humidity, and airflow at every fraction of a millimetre of the crystal's journey from cloud to ground determine its precise shape. Yet all snowflakes share the same hexagonal symmetry, arising from the molecular geometry of ice and the way water molecules bond in a hexagonal lattice when they freeze.
Snowflake growth is governed by diffusion and crystal growth kinetics. Water vapour molecules diffuse from the surrounding supersaturated air toward the crystal surface, where they join the ice lattice. The six corners of the hexagonal prism grow faster than the flat faces because they protrude further into the vapour field and capture more diffusing molecules. This instability (the Mullins–Sekerka instability) generates the branching dendritic arms, with each arm growing in a slightly different microenvironment, producing complex but symmetric branching.
The temperature and supersaturation of air at each altitude determines whether snow crystals grow as thin plates, hollow columns, needles, or stellar dendrites. The Nakaya morphology diagram maps crystal shape to temperature and water vapour supersaturation, revealing that dendritic snowflakes form in a narrow temperature range around −15°C. Snowflake growth simulation using the Reiter cellular automaton model or computational diffusion-limited aggregation can reproduce the extraordinary diversity of natural snowflake forms.
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.