Claude builds 3D Hamiltonian Monte Carlo animation in one shot with anaglyphs

This post is from Bob

The sausage

So as not to bury the lead (or “lede” if you want a mid-20th-century newspaper vibe), check out the this 3D HMC animation generator.

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It can render regular animations or produce anaglyph 3D encoding (red/blue). Unless you have 3D glasses, unclick the “Anaglyph 3D” checkbox at the bottom of the upper left corner control box.

The app let you zoom in and rotate the visualization with obvious controls (explanation in the footer of the visualization). The app also lets you adjust the amount of correlation in the 3D normal distribution as well as step size, number of steps, and animation speed. Looking the long way down a highly correlated “cigar” shape is dramatic.

The 3D effect with glasses is strongest when you rotate the visualization (it’s the usual intuitive controls with instructions at the bottom of the web page) and zoom in a bit. I find that using low 3D depth looks the best. Don’t get your hopes up too much. This isn’t Dr. Strange creating buildings in 3D in a Marvel movie.

If you want to pop it up in an independent browser so you can go to full screen, here’s a link.

• 3D Hamiltonian Monte Carlo Animation

How the sausage was made

I continue to be amazed at the progress of the frontier LLMs. The demo above was the result of handing Claude Opus 4.8 (“hard” thinking mode) the following single prompt with no build up. As with the Galileo inclined plane case study I posted, which Opus one-shotted, I was expecting some back and forth and false starts.

I want to generate a 3D animation for red/blue glasses of the Hamiltonian Monte Carlo algorithm. There is a nice online visualizatuion by Chi Feng here, but it is not 3D https://chi-feng.github.io/mcmc-demo/app.html I just want the main animation—no need to calculate marginals, etc.

To start, we can use a 3D highly correlated (0.9) normal target with unit variance aligned at one end of the cigar (e.g., near (2, 2, 2) looking toward (-2, 2, 2), which will have things zoom over your shoulder and come back).

If you can generate it so that it’ll run in a web browser with controls on step size and number of steps that’d be great, but if not, choose a step size conservatively so it won’t be rejecting very often. I want it to continue multiple iterations in order to see the effect of random momentum on the trajectories. Leave balls behind wherever the sampler actually samples. When it rejects, make the ball bigger. The trajectory should be thick enough to be visible.

If it’s easier to have Python generate an animation that’s also fine. I just want to be able to render it on my desktop to show people during a talk. I just ordered 50 pairs of cardboard red/blue 3D glasses to hand out.

I was wrong. It did it in one shot. After about 10 minutes of cranking away, it produced what you are looking at. The output is a self-contained (i.e., encapsulated) HTML file of 627KB. There are some things I’d change in an iteration (smaller pipes, fewer of them lying around), but I think it’s worth sharing the output of such a simple prompt. Perhaps needless to say, a follow up prompt gave me the HTML I needed to embed the result in this page as an iframe.

I wrote all 692 words of the blog post myself (other than the html embedding), but I’m sure Claude could have done that, too. The LLMs have fewer rhetorical tics when writing technical and scientific material. But it wouldn’t have sounded like me.

Statistical visualization in the mid 2020s?

I wonder what Andrew’s statistics visualization class would look like in 2026 with LLM-powered visualizations this easy to make. Now that the LLMs can reliably one-shot something this complex, I’m finally starting to worry about the future of programmers. Undergraduate enrollments in CS are very volatile and already going back down as they did after the dot com bubble burst. There was huge growth (a factor of two to three) from after the mortgage market bubble burst around 2007 until it started to decline again due to AI.