Random Walks with Pi

Much work has been done to create images from the digits of π (3.1415926…); in honor of Pi Day, here are a few of mine.


I generated a random walk using the first 10,000 digits of π (after the decimal point).  To do this, I let 0 be represented by a segment drawn to the right, 1 be a segment drawn 36 degrees counter-clockise from the horizontal; 2, 72 degrees and so on, up through 9, which is 324 degrees counter-clockwise (or 36 degrees clockwise).  It’s called a random walk because the path resembles what a person might do if walking around randomly.  The path begins in the red and ends in the blue.  Here is a magnification of the beginning, showing the first 1, at the lower center.

There’s no inherent reason to only use one digit at a time.  In the next walk, I took 20,000 digits in pairs, the first three being 14, 15, and 92.  Now, there are 100 different segment angles, each differing by 3.6 degrees from the next.

And finally, here is a walk using 50,000 digits, taken in groups of five (14159, 26535, etc.), for 100,000 possible angles.  Still looks random to me.