visualization of Pi

Interesting Pi visualization from a different angle

This image has landed on my facebook feed (original source). The lines connect neighboring digits in the decimal representation of Pi for 10000 digits. A lot of people has commented how the Pi is special and beautiful. They are right but the special feature of Pi in this case is a bit hidden. Any sequence of independent random variables with uniform distribution would produce similar result.

There exists a special term for numbers that have this interesting property. These are called normal numbers and wikipedia says this about them:

In mathematics, a normal number is a real number whose infinite sequence of digits in every base b is distributed uniformly in the sense that each of the b digit values has the same natural density 1/b, also all possible b^2 pairs of digits are equally likely with density b^−2, all b^3 triplets of digits equally likely with density b^−3

The thing is that it is not yet proven if Pi is normal number or not. However it is tested for a vast amount of digits so the first 10000 digits really have the uniform distribution.

Because I couldn’t quickly find the transition probabilities on the internet, I have made a simple statistics myself, you can look at it here:

 

 

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