Speaking of images in the digits of pi, the sci-fi novel *Contact* by Carl Sagan (his only work of fiction, on which the Jodie Foster movie was based) has a sort of last-page epilogue where a supercomputer, grinding away at pi, discovers a “message” hidden in the digits:

*“The anomaly showed up most starkly in Base 11 arithmetic, where it could be written out entirely as zeros and ones…The program reassembled the digits into a square raster, an equal number across and down. The first line was an uninterrupted file of zeros, left to right. The second line showed a single numeral one, exactly in the middle, with zeros at the borders, left and right. After a few more lines, an unmistakable arc had formed, composed of ones. The simple geometrical figure had been quickly constructed, line by line, self-reflexive, rich with promise. The last line of the figure emerged, all zeros except for a single centered one. The subsequent line would be zeros only, part of the frame.*

*“Hiding in the alternating patterns of digits, deep inside the transcendental number, was a perfect circle, its form traced out by unities in a field of noughts.*

*“The universe was made on purpose, the circle said. In whatever galaxy you happen to find yourself, you take the circumference of a circle, divide it by its diameter, measure closely enough, and uncover a miracle—another circle, drawn kilometers downstream of the decimal point. There would be richer messages farther in…”*

(c) 1985 by Carl Sagan, Simon & Schuster, New York*