The different shapes and sizes of snowflakes have been eluding scientists and mathematicians ever since the 17th century. Though they exist in multiple shapes, one of the most mysterious aspects of the natural snowflake growing process is why don't they produce an even wider range of crystal types. For the first time a mathematician and computer scientist from UC Davis in collaboration with colleagues from the University of Wisconsin-Madison have developed a program in which a snowflake is being modeled by a computer desktop.

In 1611, Johannes Kepler during a study of the snowflake shape, that of the dendritic type, suggested that structure actually reflects the image of an underlying crystal. The new mathematical model constructed and implemented by Janko Grayner shows that though no two crystals are identical, they share many similar features.

Usually, snowflakes developing in the Earth's atmosphere require a starting structure on which the nucleation process to take place. Water vapors floating through the air meet dust particles and condense on them. If the temperature is low enough than it will form a base crystal which will grow, as other water molecules are attached and detached from the base crystal. The computer simulation had to be able to point out that newly attached molecules to crystal take preferential places, such as the concavities in the crystal base.

The same mathematical model provided an explanation related to the crystal variety. It seems that the basic crystal shape is greatly affected by multiple atmospheric factors, such as temperature and pressure, but water vapor density as well.

A mathematical model of a snowflake crystal constructed molecule by molecule is basically impossible with the current computing power available. Grayner estimates that even with the final configuration of the computer program, it would still take about one full day for a typical desktop computer to process all the data and accurately recreate the three-dimensional image of a dendritic snowflake.

The computer model is able to reproduce all the known snowflake shapes. However, as in nature, dendritic snowflake are relatively rare. Another snowflake type extremely rare and unstable in nature is that of the butterfly shape that appears in the form of three butterflies stuck together along a single central body. It seems that snowflakes involve extremely complex spacial structures, which usually form between two plates, features observed with the help of electron telescopes.