10182

# Digits Walks of Transcendental Numbers

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.

### DETAILS

Normality of numbers is the subject of ongoing studies and a walk may only be a first indication of whether a number is normal.
Snapshot 1: was proved to be 2-normal and its walk wanders close to the origin
Snapshot 2: has a completely different patterned walk and was nevertheless proven to be 2-normal
Snapshot 3: has a walk similar to but has not proven to be normal yet
Reference
[1] A. Belshaw and P. Borwein. "Champernowne’s Number, Strong Normality, and the X Chromosome." Centre for Experimental and Constructive Mathematics. www.cecm.sfu.ca/personal/pborwein/PAPERS/P236.pdf.

### PERMANENT CITATION

 Share: Embed Interactive Demonstration New! Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details » Download Demonstration as CDF » Download Author Code »(preview ») Files require Wolfram CDF Player or Mathematica.

#### Related Topics

 RELATED RESOURCES
 The #1 tool for creating Demonstrations and anything technical. Explore anything with the first computational knowledge engine. The web's most extensive mathematics resource. An app for every course—right in the palm of your hand. Read our views on math,science, and technology. The format that makes Demonstrations (and any information) easy to share and interact with. Programs & resources for educators, schools & students. Join the initiative for modernizing math education. Walk through homework problems one step at a time, with hints to help along the way. Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet. Knowledge-based programming for everyone.