Generate a snow flake pattern Excel [holiday fun]

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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.

snow-flakes-in-excel-demo

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.

  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.