This is a walk made out of the first 100 billion digits of pi in base 4 with the following rules for the steps:

- 0 right

- 1 up

- 2 left

- 3 down

The color indicates the path followed by the walk: it starts at red and moves up the spectrum (red-orange-yellow-green-cyan-blue-purple-red) as the walk progresses. After 100 billion steps it is close to where it started. It is unknown whether the digits of pi are random, although it is generally believed that they are. The picture clearly supports this conjecture: it shows a seemingly 'random' walk.

For more details, see walks.carma.newcastle.edu.au /

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Image created at CARMA (Priority Research Centre for Computer-Assisted Research Mathematics and its Applications)

The University of Newcastle

Australia