I thought that it would be interesting to see what the digits of π look like if we alternate between adding and subtracting them by their position. Use alternating signs by position: +3, then -1, +4, -1, ... (each even index adds, each odd index subtracts). When I created this chart, I expected to see a random sequence around zero, but instead, I was surprised to find these patterns and clusters of positive and negative values. It also showed me that this sequence tended to produce more positive values near the start of the values (up to about index 50K), which is quite unexpected for a number that is often considered to be "random". This chart has made me woonder whether there are any mathematical explanations for these patterns.
By James Davies, for Pi Day 38 (March 14, 2024)