As I went through a laptop upgrade and migration recently, I discovered remnants of my old academic webpage. I found this post which has some pretty diagrams for simulations of Brownian motion and related mathematical objects. I thought it could be interesting to reproduce so that these pretty diagrams don’t get lost forever! Incidentally, I really enjoyed learning about Brownian motion, and I revisit my lecture notes from time to time.

In this page, you will find a few small simulations I ran about Brownian motion and related processes. I just think it looks cool. Don’t expect any kind of real explanation of what is going on. I learned most of what I know about Brownian motion from Louigi Addario-Berry’s Fall 2016 course on Brownian motion, largely based on the free book by Peter Mörters, and Yuval Peres.

I had some fun over the last week preparing a gender-swapped version of EarthBound for the SNES. I made use of the excellent tool CoilSnake, which can be used to patch and rebuild an EarthBound ROM with modified assets and scripts.

The full set of changes includes things like:

• gender swapping all Ness sprites, replacing his baseball cap with a red bow. Includes changes to Ness robot sprites, cycling sprites, climbing sprites, etc. There were maybe a dozen or so sprites that needed adjustment.

I’ve been messing around in my free time doing a bit of coding for fun and to explore areas of interest. It’s a bit hard to motivate myself to code during my free time considering coding is also part of my day job. But my day job is not very technically interesting, so this is how I get to explore the fun of coding. I’ll briefly describe a few of these projects which I have in mind.

I decided yesterday to rebuild this website using Hugo, while it was originally built using Jekyll. In this post I’ll discuss my experience.

galtonwatson is a Go module in early development which implements efficient algorithms for the generation and manipulation of Galton-Watson trees. By extension, this tool can be used to generate uniformly random samples from many classes of rooted trees, including:

• uniformly random binary trees of a given size,
• uniformly random d-ary trees of a given size,
• uniformly random Cayley trees, i.e., unordered labeled trees of a given size,
• uniformly random ordered trees of a given size,
• etc.