How Science Works | Why Snowflakes Grow into Different Shapes

The word “snowflake” is used loosely. Sometimes it means one intricate ice crystal; sometimes it means a falling cluster containing many crystals stuck together. To understand the origin of a six-armed pattern, first follow a single crystal growing from water vapour.

Water molecules in the gas move through air and can become incorporated into solid ice. This gas-to-solid process is called deposition. It differs from freezing a liquid droplet, even though freezing can help produce an initial ice particle. Once a seed exists, subsequent growth can add much more material and transform its outline.

Not every falling piece of snow remains a pristine single crystal. Crystals can collide and stick, break, collect liquid droplets, partly melt or lose mass to the air. A lumpy particle is therefore not necessarily an unsuccessful version of a perfect star. It may have experienced a different sequence of processes.

NOAA’s National Severe Storms Laboratory distinguishes aggregates from graupel. Aggregates contain joined snow crystals. Graupel develops as supercooled liquid droplets freeze onto an ice particle, a process called riming. Those added droplets can obscure the original crystal shape.

For our first question, set these complications aside: how does an isolated crystal acquire plates, columns and branches while growing from vapour? We will bring its later collisions and environmental history back into the explanation after establishing the basic geometry.

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Ordinary atmospheric ice commonly has a hexagonal crystal structure. Its water molecules occupy an ordered three-dimensional arrangement. That repeated arrangement helps explain why six equivalent directions appear around the central axis of many snow crystals.

A useful starting shape is a hexagonal prism. Imagine a pencil with a six-sided cross-section, except that it can be extremely short and wide or long and narrow. The two end faces are called basal faces. The six side faces are prism faces. These names identify orientations in the crystal rather than different materials.

The prism picture immediately corrects an important misconception: “hexagonal” does not mean “a flat six-pointed star”. A compact plate without arms and a column viewed from its end can both reveal hexagonal order. A side view of the same column may appear mainly rectangular.

Draw a regular hexagon and mark lines from its centre to its six corners. A complete turn is 360 degrees, so equally spaced directions are separated by 360/6 = 60 degrees. That angular pattern reflects an idealised symmetry. It does not specify how far each arm must extend or how many sidebranches must appear.

A paper snowflake cut from folded paper repeats the same cut by construction. A growing snow crystal has no equivalent folding operation. Its regions encounter similar large-scale conditions, but local fluctuations, defects and later damage can make them different. Sixfold molecular order constrains possibilities without guaranteeing a perfectly symmetric outer boundary.

This distinction is essential when comparing photographs. A recognisable crystal symmetry is evidence about its underlying organisation. Exact mirror-image arms would be a much stronger claim about its entire growth history.

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A crystal grows when its surfaces move outward as new molecules join. The direction in which a face advances is perpendicular to that face. A face’s area and its outward growth speed are different quantities.

If the two basal faces move apart rapidly, the prism lengthens along its central axis. If the prism faces advance outward rapidly while basal advance is slow, it spreads sideways into a plate. Thus a broad face can remain visible precisely because growth perpendicular to it is comparatively slow.

An original geometric model makes the distinction concrete. Begin with a prism 10 micrometres thick and 10 micrometres across opposite side faces. For a fictional ten-second interval, let each basal face advance at 0.1 micrometres per second and each opposing prism face advance at 1 micrometre per second.

Thickness increases on both ends: 10 + 2 × 0.1 × 10 = 12 micrometres. Width also increases on both sides: 10 + 2 × 1 × 10 = 30 micrometres. Its thickness-to-width ratio is 12/30 = 0.40, so it has become plate-like.

Reverse the two chosen speeds. Thickness becomes 30 micrometres and width becomes 12 micrometres, giving a ratio of 2.5 and a column-like shape. Both objects retain the same basic crystal orientations; their different proportions follow from different directional growth rates.

These arbitrary constant speeds demonstrate geometry only. Real surface speeds depend on local conditions, crystal size and molecular attachment processes, and may change during the interval. The example does not assign a temperature to either shape. That connection requires measurements of actual ice growth.

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Temperature matters, but so does the amount of water vapour available relative to equilibrium with ice. Supersaturation with respect to ice describes an excess above that reference value at the specified temperature.

One definition is the actual water-vapour pressure divided by the equilibrium vapour pressure over ice, minus one. Multiplying by 100 expresses it as a percentage. The reference must be stated: equilibrium over liquid water and equilibrium over ice differ below freezing.

Use deliberately hypothetical pressures to practise the arithmetic. If equilibrium over ice at a chosen temperature were 200 pascals and the surrounding vapour pressure were 210 pascals, the excess would be 10 pascals. Supersaturation would be (210/200 − 1) × 100 = 5%. Relative humidity with respect to ice would be 105%.

Now hold actual vapour pressure at 210 pascals but imagine conditions for which the equilibrium ice value is 205 pascals. Supersaturation becomes (210/205 − 1) × 100, approximately 2.44%. The vapour amount expressed as pressure has not changed, but its relationship to the reference has. Neither chosen equilibrium value is offered as a real temperature lookup.

The calculation shows why “humid” alone is an incomplete description of a growth environment. Researchers need temperature and a clearly defined moisture measure. A room-weather humidity reading referenced to liquid water cannot simply be substituted for ice supersaturation without checking the definition.

There is also a spatial distinction. A growing crystal consumes nearby vapour. Supersaturation immediately at its surface can be lower than the value farther away. Interpreting a growth rate therefore requires both transport through air and incorporation into ice, rather than treating the surrounding humidity reading as the complete molecular story.

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Molecules that reach an ice surface do not all immediately occupy their final lattice positions. Joining an ordered solid involves surface processes, including movement along surfaces and the formation or extension of molecular layers. Different crystal faces can respond differently to temperature and vapour conditions.

Laboratory observations are summarised in a morphology diagram, often called the Nakaya diagram. Under commonly studied atmospheric-pressure conditions, plate-like growth occurs near −2°C, column or needle-like growth near −5°C, and plate-like growth again near −15°C. These are illustrative regions, not exact universal boundaries or a rule that colder always means thinner.

At a given temperature, changing supersaturation can also change the degree of complexity. Relatively slow growth can yield compact faceted forms; stronger growth can favour more elaborate structures. Caltech’s free-falling crystal observations show how laboratory-grown populations differ between temperatures and vapour conditions, while still containing variation within a treatment.

Why does the preferred shape switch more than once as temperature falls? “Cold water freezes” does not answer that question. The explanation must account for the relative growth of basal and prism surfaces and how their attachment behaviour changes.

Libbrecht’s physical model of the morphology diagram proposes a role for surface diffusion, facet width and surface premelting in producing that complex dependence. The linked work is a primary research preprint. It provides a mechanistic framework rather than permission to treat every microscopic detail as settled.

The appropriate confidence levels differ: the broad temperature-dependent patterns are experimentally observable; detailed molecular models are tested by how well they reproduce rates, shapes and changes under controlled conditions. A colourful diagram summarises observations, but it cannot by itself explain their cause.

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A flat plate need not remain a compact hexagon. As water vapour diffuses through the surrounding air, protruding regions can have better access to the supply than recessed regions. A corner that extends outward may grow faster, making it project farther and strengthening the difference.

This is a growth instability: a small difference in shape can be amplified. As a main arm develops, smaller protrusions along it can become sidebranches. The result resembles a tree, which is why branched forms are called dendritic.

Libbrecht’s explanation of branching describes this competition between faceted growth and protrusion-enhancing transport. Branching alone would not explain the characteristic crystallographic directions; molecular surface behaviour and vapour diffusion act together.

For a labelled diagram, draw three successive stages. First show a compact hexagonal plate with a surrounding vapour field. Next extend its six corners slightly, marking arrows from nearby air towards the protrusions. Finally lengthen those protrusions into arms, adding smaller branches behind the tips. Label the arrows “net vapour transport”, not “molecules aiming at corners”. Individual molecules move randomly; the collective transport responds to concentration differences and geometry.

The diagram is conceptual, not a flow map or a molecular trajectory calculation. A real field depends on the full three-dimensional crystal and neighbouring conditions. Recessed regions still receive molecules; they are not permanently shut off.

A mathematical Koch snowflake repeatedly adds identical geometry at smaller scales. A real ice crystal does not follow that drawing instruction. Its branching occurs over a finite range of sizes and depends on changing physical conditions. Calling its appearance fractal may describe a resemblance, but does not supply the mechanism that produced it.

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Why can six branches look remarkably similar if they grow locally? They belong to a single small crystal and often experience approximately the same changing temperature and surrounding vapour conditions. A shift in growth regime can therefore affect all of them around the same time.

Imagine a hypothetical crystal that first develops a simple plate, then encounters conditions favouring branching, then spends time in a slower-growth regime. Its centre and outer regions need not share the same appearance because they formed during different stages. The outline combines processes in sequence.

Now compare two hypothetical journeys with the same average temperature. In Journey A, an interval favouring column growth comes first and an interval favouring plate growth comes second. Journey B reverses the order. Equal averages do not imply equal shapes: the structure already present influences the surfaces available for later growth.

A capped column, for example, combines a columnar centre with plates at its ends. Such composite forms make sense when crystal history is considered, rather than assigning the entire object to one immutable shape category. Caltech’s crystal-image discussion includes this form and connects varied morphologies to growth conditions.

This history dependence also limits reverse inference. A photograph may support a plausible sequence of regimes, but it rarely identifies a unique path, exact altitude record or complete temperature time series. Different combinations of duration, vapour supply and initial form can yield similar visible features.

Nor must every arm follow the same microscopic history. Local fluctuations, asymmetric air flow or a collision can affect one region differently. Symmetry is an approximate outcome of shared structure and environment, not evidence that branches exchange instructions.

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A beautiful image establishes that a shape exists. Testing a growth explanation requires additional information: initial crystal form, temperature, supersaturation, elapsed time, dimensions and measurement uncertainty. Those variables let researchers compare predictions rather than merely recognise familiar outlines.

In their primary measurements of ice growth at −5°C and −10°C, Libbrecht and Arnold measured crystals grown in a free-fall chamber and compared dimensions with numerical models. Their report discusses errors caused by environmental calibration, sampling and changes after crystals landed. In particular, delayed observation had previously mimicked an early rapid-growth period. Correcting that issue changed the interpretation.

This is an unusually useful lesson in how science works. A measured pattern can arise from the specimen’s growth or from the measurement sequence. Recording elapsed time means specifying elapsed time until what event: arrival on a surface, first image or final measurement?

A later 2023 primary research preprint quantifying the Nakaya diagram presents 206 growth observations spanning temperature and supersaturation. Crystals grew from defined ice-needle seeds for known times. That design enables quantitative model comparisons across many conditions, while its supported-growth arrangement should not be confused with every freely falling atmospheric crystal.

An informative model must predict more than “some branches appear”. It should account for dimensions, relative face growth and changes when a controlled variable is altered. A model adjusted separately to reproduce every photograph has weaker predictive value than one that also succeeds on new conditions.

Laboratory control does not erase uncertainty. It makes the uncertain quantities visible enough to investigate. Comparing different experimental arrangements is valuable precisely because each arrangement has its own potential biases.

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Begin by deciding what the image actually shows. Is it a single crystal, an aggregate or a rimed particle? Is there a scale bar? Is the object viewed from above, from the side or at an angle? A plate seen edge-on can look deceptively narrow.

Next separate observation from interpretation. “Six prominent arms with unequal lengths” is an observation. “This crystal passed through changing growth conditions” is an interpretation consistent with many structures. “It spent exactly three minutes at a particular temperature” would require far more evidence than the image supplies.

A safe classroom exercise can use already published photographs without collecting snow or constructing a cold chamber. Select three images from the researcher’s SnowCrystals collection. For each, record overall shape, obvious symmetry, signs of aggregation or riming if visible, and whether scale and viewing direction are given. Mark uncertain features rather than forcing every object into a category.

Then compare two ways of assembling the sample. Choosing the three prettiest stars answers a question about striking examples. Choosing images by a fixed rule, such as the first three suitable documented specimens in a collection, reduces one kind of aesthetic selection. Neither becomes a representative survey of natural snowfall unless the original collection method supports that claim.

This matters for the familiar claim that every snowflake is unique. Complex natural crystals can differ enormously, but a finite photographic sample cannot prove that no two crystals have ever matched at every conceivable level of detail. “Identical” also needs a definition: same broad category, same microscope outline or same molecular arrangement are different tests.

A useful investigation therefore asks a measurable question about similarity instead of relying on an absolute slogan.

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Why six directions? The ordered structure of common hexagonal ice supplies equivalent orientations. It does not require six long arms, perfectly matching branches or a flat crystal.

Why a plate rather than a column? The relative rates at which basal and prism faces advance determine the proportions. Faster lateral expansion makes a plate; faster growth along the central axis makes a column. Temperature and supersaturation influence those rates through surface and transport processes.

Why branches? Protrusions can gain better access to diffusing vapour and grow into larger protrusions. Crystallographic growth behaviour channels that instability into characteristic patterns, while local fluctuations introduce variation.

Why different final shapes? Crystals begin differently, encounter different conditions for different durations, and may undergo collisions, riming, melting or sublimation. The final object combines molecular structure with a history of physical events.

Return to the worked prism in Chapter 3. If both pairs of opposing faces instead advanced at the same constant speed, the initially equal thickness and width would remain equal in that simplified model. That result does not claim all real equally supplied ice crystals remain compact. It shows which difference our geometric example deliberately introduced to create different proportions.

The strongest explanation joins a mechanism to an observation and keeps its limits visible. A morphology diagram organises repeatable patterns. A growth model tries to explain them. Carefully timed measurements test the model. A photograph becomes much more informative when those layers are kept distinct.

Continue to Cryosphere Science for what happens after snow accumulates, changes within the snowpack and becomes part of Earth’s larger frozen-water system.

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