Snowflake in the context of "Snow"

In philosophy, systems theory, science, and art, emergence occurs when a complex entity has properties or behaviors that its parts do not have on their own, and emerge only when they interact in a wider whole.

Emergence plays a central role in theories of integrative levels and of complex systems. For instance, the phenomenon of life as studied in biology is an emergent property of chemistry and physics.

Graupel (/ˈɡraʊpəl/; German: [ˈɡʁaʊpl̩] ), also called soft hail or hominy snow or granular snow or snow pellets, is precipitation that forms when supercooled water droplets in air are collected and freeze on falling snowflakes, forming 2–5 mm (0.08–0.20 in) balls of crisp, opaque rime.

Graupel is distinct from hail and ice pellets in both formation and appearance. However, both hail and graupel are common in thunderstorms with cumulonimbus clouds, though graupel also falls in winter storms, and at higher elevations as well. The METAR code for graupel is GS.

Firn (/ˈfɪərn/; from Swiss German firn "last year's", cognate with before) is partially compacted névé, a type of snow that has been left over from past seasons and has been recrystallized into a substance denser than névé. It is ice that is at an intermediate stage between snow and glacial ice. Firn has the appearance of wet sugar, but has a hardness that makes it extremely resistant to shovelling. Its density generally ranges from 0.35 g/cm to 0.9 g/cm, and it can often be found underneath the snow that accumulates at the head of a glacier.

Snowflakes are compressed under the weight of the overlying snowpack. Individual crystals near the melting point are semiliquid and slick, allowing them to glide along other crystal planes and fill in the spaces between them, increasing the ice's density. Where the crystals touch, they bond together, squeezing the air between them to the surface or into bubbles.

The identity of indiscernibles is an ontological principle that states that there cannot be separate objects or entities that have all their properties in common. That is, entities x and y are identical if every predicate possessed by x is also possessed by y and vice versa. It states that no two distinct things (such as snowflakes) can be exactly alike, but this is intended as a metaphysical principle rather than one of natural science. A related principle is the indiscernibility of identicals, discussed below.

A form of the principle is attributed to the German philosopher Gottfried Wilhelm Leibniz. While some think that Leibniz's version of the principle is meant to be only the indiscernibility of identicals, others have interpreted it as the conjunction of the identity of indiscernibles and the indiscernibility of identicals (the converse principle). Because of its association with Leibniz, the indiscernibility of identicals is sometimes known as Leibniz's law. It is considered to be one of his great metaphysical principles, the other being the principle of noncontradiction and the principle of sufficient reason (famously used in his disputes with Newton and Clarke in the Leibniz–Clarke correspondence).