A Procedure to Compute the Digit Sequence of a Square Root

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.

THINGS TO TRY

SNAPSHOTS

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