Counting Polycubes of Size 21

There are 1,636,229,771,639,924 unique 3D polycubes that can be constructed with 21 cubes.

I calculated this number over a period of 10 days in the Amazon Elastic Compute Cloud using Stanley Dodds's amazing algorithm (see below), which I ported to rust. In this post I'll give some background on my efforts to compute this value.

The canonical source of many integer sequences, including many polycube and polyomino sequences, lives at the OEIS. The relevant sequence here (polycubes containing $n$ cubes) is sequence A000162, where you'll find the rest of the known values in this sequence as well as a link to Dodds's code.

New Gallery Pages

New photo gallery pages are now available!

It's that time of year for photographers... dealing with the mountain of images created during the year. Along those lines, this seemed like a good time to work on a way to showcase my non-birding photos, and to finally make it a bit easier to navigate among the galleries published here.

First, I went through my 2021-2023 archive and put my favorite non-bird photos into yearly galleries. Here's the 2023 gallery.

Then, for navigation I've created a new Photo Galleries Page with links to all galleries.

NFL Elo Models Compared

Yesterday, I published an update to my NFL Elo rating model, and today I published the "after week 6" ratings and rankings.

In this post, I'd like to compare the accuracy stats for three different models.

NFL Elo Power Rankings for 2023

I've been working on code to calculate Elo ratings for NFL teams, and thus Elo-based power rankings, for the last couple weeks.

The power rankings page for the current season is available here.

Trying Generative Fill in Photoshop

The year is 2023. Machine learning is all the rage (for good reason, I believe).

Computer-generated graphics is one area where the computing industry is experimenting with ML. I recently installed the Photoshop beta, which gives access to this tech through its new "generative fill" feature. I tested the feature out on some recent photos of mine.