A Procedure to Compute the Digit Sequence of a Square Root

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration visualizes a procedure for generating the base-2 digit sequence of a square root. From A New Kind of Science, p. 141: "To find , start by setting and . Then at each step apply the rule . The result is that the base-2 digits of turn out to correspond exactly to the digits of . If is not between 1 and 4, it must be multiplied or divided by an appropriate power of 4 before starting the procedure."


The digit sequence of r is shown on the left, while the digit sequence of —which corresponds exactly to —is shown on the right. Black cells represent ones, and gray cells represent zeros.


Contributed by: Abigail Nussey (March 2011)
Open content licensed under CC BY-NC-SA



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.