Our images of the week show the amazing snow art created by Simon Beck.

Snow art. Image © Simon Beck.

The Von Koch snowflake. |

Simon Becks' book, |

Beck creates those beautiful geometrical shapes by walking through the snow. The shape you see above is based on the *Von Koch snowflake*. To create the full shape, you start with an equilateral triangle and replace the middle third of each side by a "spike" consisting of two sides of a smaller equilateral triangle. Now do the same for each of the twelve straight-line segments of the resulting shape and repeat, ad infinitum. The Von Koch snowflake is an example of a *fractal*, a mathematical shape that is infinitely intricate and self-similar: it exhibits the same structures over and over again as you zoom in on smaller and smaller pieces. You can find out more about fractals here.

Beck can't produce the Von Koch snowflake exactly, of course, because it involves an infinite process. But he has created an amazingly good approximation, which comes from using the first few iterations of the process. He gets the shape down in the snow by counting steps to measure distances and using a compass when changing direction to make sure he gets the correct angles between straight-line segments. "In the case of the Koch shape, I found I was soon able to judge the 60 degree angles and do it quicker to an acceptable level of accuracy without using the compass," he says.

If you like the pictures, you can see more of them in Beck's new book, *Snow Art*, which you can purchase from his website. Here are a few more samples:

Image © Simon Beck.

Image © Simon Beck.

Image © Simon Beck.

Image © Simon Beck.

You can see previous images of the week here.