Hamming Distance Sequences (OEIS)

My friend Mithra Karamchedu and I were learning about metric spaces and, as a simple exercise, tried to prove that hamming distance is a metric (we failed—it isn't). What started as a casual weekend project turned into a fun side quest. We coded up a couple of simulations, did some math exercises, found some interesting fractal-like structure, submitted it to the OEIS, and it got published, which was neat. This is an example of one of my more out-there, unrelated projects, but it was really cool.

Abstract

The hamming distance between two strings is the number of positions at which the corresponding symbols are different. During our exploration, we discovered interesting fractal-like patterns and sequences that hadn't been documented before.

After verifying our findings and following the proper submission process, we contributed two new sequences to the Online Encyclopedia of Integer Sequences (OEIS): A365618 and A367055.