# Mathematical Model Computes Snow Flake Shapes for the First Time

## Some snow flakes shapes are so complex that no computer model has ever been able to generate them. Until now.

Feb 15, 2012
Back in 1954, the Japanese physicist Ukichiro Nakaya published a landmark study on the nature of snowflakes. He classified flakes into various categories and even discovered how to grow them in laboratory conditions, the first time this had been done.
Nakaya discovered snow flakes form when supersaturated vapour cools below zero but also that their shape is highly sensitive to both the level of supersaturation and the temperature. His diagram (above) summarising his results, has since become famous.
Since then, various researchers have attempted to better understand the processes that determine snowflake morphology. In this blog, for example, we’ve looked at the work of Kenneth Libbrecht, one of the world leaders in this area.
One challenge in this field is to simulate the growth of snowflakes of all shapes with a computer model. However, success has been hard to come by because of the difficulty in modelling the complex conditions that exist at the ice/air boundary as a crystal grows.
In particular, modellers have found it hard to capture the simultaneous growth of facets with the dendritic branching that occurs when flakes grow. When combined, these processes are thought to generates many of the famously beautiful crystal shapes.
Today, John Barrett at Imperial College London and a couple of pals reveal their approach to snowflake modelling, which they say solves this problem.
The result is that they have been able to compute various snow flake shapes that appear in nature for the first time. These include solid plates, solid prisms, hollow columns, needles, dendrites, capped columns and scrolls on plates.
The model also provides some insight into how the crystals form. For example, their model predicts  a linear relationship between the velocity of crystal tip growth and the degree of supersaturation.
That’s something that could be tested in the lab. And Libbrecht, for example, has the gear to do the job.
Ref: arxiv.org/abs/1202.1272: Numerical Computations Of Facetted Pattern Formation In Snow Crystal Growth