They might have been using the fast multipole expansion method

Thanks so much, really appreciate it! I’ve been focusing the presets on stable or interesting solutions that aren’t tied to real systems, but adding a few real examples like Alpha Centauri would fit in nicely. I’ll keep that on the list for future updates.

It destabilized after a few minutes on my phone.

Thank you! Your 2D version is great, I love seeing how different people approach this stuff. As for integrators, I currently only have Velocity Verlet and RK4 (can change in the advanced settings). I started with just Verlet, but to get some of the presets to behave properly I ended up needing RK4 as well. I’ve been thinking about adding adaptive methods next, but I'll take a look at the methods you've got listed too. Everything is still running in plain JS for now. I started moving some of the work into web workers but haven’t finished that part yet.

I would be very curious to compare notes on the integrators you used. How good do they perform in general?

In the avobed shared you can go to the settings a pick an integrator. I did the integrators in wasm although I suspect js is just as fast.

Color me impressed! I love the ammount of settings you can play with. I still need to understand what happens whe yu add more bodies though.

Thanks! The Three-Body series definitely helped spark the idea, and the URL is a little nod to the books. I also took some simulation classes back in college, so the math and physics side pulled me in too. It’s crossed my mind that it could be fun to add a kind of Trisolaran mode that tracks a small planet and how habitable its position is throughout the orbits.

I think the URL is telling

It might be fun to add some kind of visualization showing when a body has enough energy to potentially escape the system.

> However, some of these were misleading. I had one running for 15 minutes at 5x, and the third body did eventually return.

That's not misleading. Real three-body orbital systems show this same behavior. Consider that such a system must obey energy conservation, so only a few extreme edge cases lose one of its members permanently (not impossible, just unlikely).

Ironically, because computer simulators are based on numerical DE solvers, they sometimes show outcomes that a real orbital system wouldn't/couldn't.

There’s a big one in the sky right now - the Earth-Moon-Sun system.

No, and please don’t try to learn anything from that science-free series. The author doesn't even have a Wikipedia-level understanding of what he is writing about.

N-body problems for N>3 do not have exact, closed form solutions. For N=2 the solution is an ellipse. For N=3+ there is no equation you can write down that you can just plug in t and get any future value for the state of the system.

But that is NOT the same as saying it is unpredictable. It is perfectly predictable. You just have to use one of the many numerical solutions for integrating ODEs.

The link points to one of the stable solutions, and there are actually quite a few of those. The problem is that there’s no general closed form that tells us exactly where the bodies will be in the future, so we rely on numerical methods to approximate the motion. If you hit Reset All a few times or add more bodies, you’ll start to see the chaos

> No physics expert but isn't this unpredictable (based on what I saw in series) ?

A three-body orbital problem is an example of a chaotic system, meaning a system extraordinarily sensitive to initial conditions. So no, not unpredictable in the classical sense, because you can always get the same result for the same initial conditions, but it's a system very sensitive to initial settings.

> Amd this does seem predictable, I saw this for almost a minute

The fact that it remains calculable indefinitely isn't evidence that it's predictable in advance -- consider the solar system, which technically is also a chaotic system (as is any orbital system with more than two bodies).

For example, when we spot a new asteroid, we can make calculations about its future path, but those are just estimates of future behavior. Such estimates have a time horizon, after which we can no longer offer reliable assurances about its future path.

You mentioned the TV series. The story is pretty realistic about what a civilization would face if trapped in a three-solar-body system, because the system would have a time horizon past which predictions would become less and less reliable.

I especially like the Three Body Problem series because, unlike most sci-fi, it includes accurate science -- at least in places.

> Is this with Gemini 3?

An LLM couldn't provide results for a sim like this, compared to a relatively simple numerical differential equation solver, which is how this sim works. Unless you're asking whether a sim like this could be vibe-coded, if so, the answer is yes, certainly, because the required code is relatively easy to create and test.

Apart from a handful of specific solutions, there are no general closed-form solutions for orbital problem in this class, so an LLM wouldn't be able to provide one.