WOLFRAM|DEMONSTRATIONS PROJECT

Digits Walks of Transcendental Numbers

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number
Champernowne
π

2
digits
1000
base for Champernowne
3
A "walk" on the digits of a number can be used to evaluate the normality of a transcendental number in base 2 [1].
In this Demonstration a two-dimensional walk with unit steps is created by blocking the binary digits into pairs and assigning each of the four possible pairs to one of the four directions: northeast, southeast, southwest, and northwest. The walk of a base-2 normal number is expected to resemble a random walk and should not wander increasingly far from the origin.