This Demonstration visualizes a procedure for generating the base 2-digit sequence for the rational number

,

,

. From

*A New Kind of Science*, p. 139: "The idea is to have a number

which essentially keeps track of the remainder at each step in the division. One starts by setting

equal to

. Then at each step, one compares the values of

and

. If

is less than

, the digit generated at that step is 0, and

is replaced by

. Otherwise,

is replaced by

. With this procedure, the value of

is always less than

. And as a result, the digit sequence obtained always repeats at most every

steps." On the left, the

row shows the binary digits of

at the

step in the algorithm, and on the right, the binary digits of

are shown vertically. Black cells represent 1's, and gray cells represent 0's.