It would be fitting to use Circos to visualize the digits of pi, since what is more round than Circos? Circos is a software package for visualizing data and information. It visualizes data in a circular layout — this makes Circos ideal for exploring relationships between objects or positions.
The position of the link on a digit's segment is associated with the position of the digit π. For example, the "14" link associated with the 2nd digit (1) and the 3rd digit (4) is drawn from position 2 on the 1 segment to position 3 on the 4 segment.
As more digits are added to the path, the image becomes a weaving mandala.
For a given digit, the chance that the next 5 digits are the same is 0.00001 (0.1 that the next digit is the same * 0.1 that the second-nex digit is the same * ...). Therefore the chance that a given position the next 5 digits are not the same is 1 - 1/0.00001 = 0.99999. From this, the chance that k consecutive digits don't initiate a 6-digit sequence is therefore 0.99999k.
If I ask what is k for which this value is 0.5, I need to solve 0.99999k, which gives k = 69,314. Thus, chances are 50-50 that in a 69,000 digit random sequence we'll see a run of 6 idendical digits. This calculation is an approximation.
It's fun to look for words in π. For example, love appears at 13,099,586th digit.
Why the Brewer palette? These color schemes have some very useful perceptual properties and are commonly used to encode quantitative and categorical data.