Vibe-Coding the End of Math: Busy Beaver

A busy beaver at his computer.

Like a lot of folks, I’ve been using AI to speed up everyday tasks at work and at home, but I’ve been looking for a good excuse to sit down, vibe code, and deploy a full interactive app entirely from scratch.

Recently, I read a fascinating Quanta Magazine article about the Busy Beaver problem—a theoretical computer science puzzle that quickly escalates from simple logic into numbers that literally break the boundaries of modern mathematics. I realized this was the perfect project. I wanted to actually visualize and play this like a game, and AI could help me build the sandbox.

You can try it out right here: Play the Busy Beaver Simulator

It’s a fully functional Turing machine simulator right in your browser. You write the rules, and the little beaver 🦫 runs up and down the tape executing them. Try to leave as many 1s on the board as possible before the program halts, or load up one of the historical champion machines to see how quickly things spiral out of control.

Dock at Sunset, Ramsvik, Sweden

Dock at Sunset, Ramsvik, Sweden

I have a backlog of unpublished photos, including this gem from a prolific trip I took to Europe in 2018. On this same trip, I took a lot of favorites including several from Paris and a panorama of Stockholm. However, a folder of images remained untouched. Finally, I revisited them, and this one stood out. But where was it taken?

West Point Lighthouse Twilight, Seattle, Washington

West Point Lighthouse Twilight, Seattle, Washington

In 2019, I took a couple of wonderful sunset photos of Seattle’s West Point Lighthouse while on a business trip. I wrote about one of them in 2020, including details about how and why I ended up in this location. But I’ve long had this second version of the photo in my archives, and I’m happy to share it now.

Shoreline at Sunset, Gloucester, Massachusetts

Shoreline at Sunset, Gloucester, Massachusetts

In the northern reaches of Gloucester, Massachusetts on Cape Ann, where the Annisquam River meets the Atlantic, lies a hidden gem – a secluded stretch of coastline that offers a unique perspective on the setting sun. Unlike most Massachusetts beaches, which face eastward, this western-facing shore provides a rare opportunity to witness the sun’s descent over the land, painting the sky in a vibrant palette of colors.

Beach Moonset, Kona, Hawaii

Beach Moonset, Kona, Hawaii

While exploring Kona’s Hapuna Beach in 2019, I was looking for a scene that really inspired me. It wasn’t until I reached the end of the beach, and found this spot where it transitioned back to natural rock and trees, that I found what I was looking for. I loved the meeting of sand, rock, trees, ocean, and sky with the moon setting on the horizon. And yet I have also long struggled with this photo and feeling like it was not ready for sharing.