Estimating Whether No Two Snowflakes are Alike


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Objections to this Snowflake Theory

Readers are welcome to raise objections, and then submit all the rest of their arithmetic in their comments. We suggest starting with the following concerns.

  • This number is too high. No snowflake could have a grain of ice surrounded by air; connections are needed; and the apparent self-symmetry reduces the possibilities.
  • This number is too low. We totally ignore how thick the snowflake is, which may vary from point to point on the triangle.
  • We should examine the snowflake under a microscope, so the resolution is 50 times higher, with 2500 times more bits. This makes it harder to find identical snowflakes.
  • We should consider all the snowflakes that ever fell on Earth; so let’s multiply the annual snowfall by 4,000,000,000 years.
  • We need to sample different types of snowflakes, and use different mathematical models for each. Duplicates might be more likely given an abundance of “plate” snowflakes.


This article suggests a mathematical framework for approaching this question, rather than claiming to have the definitive solution.

To conclude: at least two visually identical snowflakes have been found, but they had a very simple shape. It is highly improbable that there are two identical snowflakes among the complex dendrites.

Snowflakes on Blue : Image by Juliancolton2 (Julian Diamond)


Introduction to the Microscope. Orange Coast College. (2012). PDF accessed December 24, 2012.

Choi, Charles Q. Two snowflakes may actually be alike. (2007). Accessed December 24, 2012.

Thangham, Chris V. No two snowflakes are alike. Digital Journal. (2008). Accessed December 24, 2012.

Weisstein, Eric W. Birthday Problem. MathWorld-A Wolfram Web Resource. Accessed December 24, 2012.

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