# Generate a snow flake pattern Excel [holiday fun]

Charts and Graphs - 5 comments

Yesterday I saw a tweet from @JanWillemTulp,

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

This is what I came up with.

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.

1. Let’s assume we have regular hexagon with unit radius (r = 1)
2. We calculate the vertices of a regular hexagon (x=sin θ & y = cos θ, where θ = {60,120,180…360})
3. 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)
4. 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)
5. Now we have 3 points for each vertex of the hexagon
1. (x1,y1) – original hexagon rotated by random degrees to right and shrunk
2. (x3,y3) – original hexagon rotated by same random degrees to left and shrunk
3. (x2,y2) – original hexagon expanded by a random factor
6. 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)
7. We repeat this process for all vertices
8. We now have a teeny tiny snow flake.
9. 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.

Hello Awesome...

My name is Chandoo. Thanks for dropping by. My mission is to make you awesome in Excel & your work. I live in Wellington, New Zealand. When I am not F9ing my formulas, I cycle, cook or play lego with my kids. Know more about me.

I hope you enjoyed this article. Visit Excel for Beginner or Advanced Excel pages to learn more or join my online video class to master Excel.

Thank you and see you around.

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 Written by Chandoo Tags: Advanced Charting, charting, Cos(), downloads, dynamic charts, mathematics, scatter plot, screencasts, Sin() Home: Chandoo.org Main Page ? Doubt: Ask an Excel Question

### 5 Responses to “Generate a snow flake pattern Excel [holiday fun]”

1. Puneet Gogia says:

Awesome Works. It can be use in some presentation work.

Thanks for sharing.

2. Modeste Geedee says:

Hi chando... 😉

another alternative approach
http://www.cjoint.com/c/ELybdK2VVbd

• Chandoo says:

cool approach. I thought about the radar chart route but did not pursue it. So much easier too. Thanks for sharing it. Happy holidays 🙂

3. Issac paul says:

Wow !!! Awesome tutorial dude. You nailed it 😀 keep sharing much more cool tutorials

4. joe shipley says:

Thanks for doing this!

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