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 genuinely fun sidequest: we coded up a couple of simulations, did some math, found some interesting fractal-like structure, submitted it to the OEIS, and it got published, which was neat. Very much one of my more out-there and unrelated projects, but a good time.
Abstract
The Hamming distance between two strings is the number of positions at which the corresponding symbols differ. Poking at sequences built from it, we found fractal-like patterns that hadn't been documented before.
After verifying the findings and going through the submission process, we contributed two new sequences to the Online Encyclopedia of Integer Sequences: A365618 and A367055.