Mathematics · Study 051
A Walk on Pi
The first 3,000 digits of pi turned into a walk: each digit picks one of ten directions. The digits are computed in your browser as you watch.
What you're looking at
Each digit from 0 to 9 is assigned a compass direction, 36 degrees apart, and the pen takes one step that way. Colour runs from orange at the start to white at the end. The digits themselves are calculated on the page with a 300 year old arctangent formula and big integer arithmetic.
The idea behind it
The path looks like a random walk because, as far as anyone can tell, the digits of pi behave like random numbers. Pi is widely believed to be a normal number, in which every digit and every block of digits appears equally often. That has never been proved, even for single digits.
Try this
Watch the path extend. The strip along the bottom shows the most recent digits being walked.
