Yesterday I saw a tweet from @JanWillemTulp,

Happy Holidays! https://t.co/iAnKXJq20a Generate your own data snowflake based on your seasonal greeting! pic.twitter.com/RHi5bLBqSF

— Jan Willem Tulp (@JanWillemTulp) December 21, 2015

That got me thinking…? Why can’t we make a snow flake pattern in Excel?

This is what I came up with.

### Download Excel Snow Flake Maker

**Click here to download the Excel workbook**. Press F9 to make another pattern. You can also make *pentagonal *snow flakes. They are very rare, so go easy on them

### Snow flakes in Excel? How…

I am a little too lazy to explain the calculations behind this. But here is the gist. Examine the calc tab in download workbook for more.

- Let’s assume we have regular hexagon with unit radius (r = 1)
- We calculate the vertices of a regular hexagon (x=sin θ & y = cos θ, where θ = {60,120,180…360})
- Then we rotate the hexagon by random degrees (between 3 to 21) on both sides, shrink r by an arbitrary fraction (20% to 80%) and calculate new vertices. Say these are (x1,y1), (x3,y3)
- We also calculate the vertices of original hexagon when r is multiplied by a random number (between 1 and 3). Say this is (x2,y2)
- Now we have 3 points for each vertex of the hexagon
- (x1,y1) – original hexagon rotated by random degrees to right and shrunk
- (x3,y3) – original hexagon rotated by
*same*random degrees to left and shrunk - (x2,y2) – original hexagon expanded by a random factor

- We then draw a line connecting the origin (0,0) to (x1,y1) to (x2,y2) to (x3,y3) and back to origin – (0,0)
- We repeat this process for all vertices
- We now have a teeny tiny snow flake.
- When you repeat steps 3 to 7 few more times and overlay all these shapes one on top, we get a nice looking snow flake.

*The logic is similar for pentagonal snow flakes. *We just use different θs in step 2

Enjoy your snow flake, or the real snow if you live in a colder country. *Alas, *in Vizag, this winter has been a mild summer. So I am going to imagine snow while lounging under fan with a book in my hands.

Happy holidays.

PS: For more visualization fun this holidays, check out Madelbrot fractals in Excel, 3D Dancing pendulums and Excel fire works.