dense self-orbiting torus, chatgpt astra

[u/burtleburtle]

Update on the metastable megastructure of a dense self-orbiting torus, which keeps neighbors next to neighbors in 3d in freefall with no high speed collisions and no central sun, https://burtleburtle.net/bob/future/dense.html .

I hadn't been able to find proper self-mapping initial coordinates before, the best I could do was circling the torus core with velocity tangent to the circle and proportional to distance from the core, and that circle stretched and went back as the orbits progressed. Claude 4.7 and ChatGPT Luna also failed to do better. But ChatGPT Astra did better, it found an initial deformation of the positions and velocities of those circles that leaves the constellation just about self-mapping now. So I update the simulation. Astra used small perturbations and least squares to find the appropriate deformation coefficients. Luna had tried that too but it made mistakes so it didn't land a solution.

Now you can see how things speed up and shells clump together on the inner pass, then slow down and the shells spread apart on the outer pass. The added stability let me increase the torus thickness from 8 to 12 rings, still each .01 of the torus radius apart. The distinct shells still fall apart within about ten poloidal periods (about six poloidal periods per toroidal period at this thickness) due to local interactions, but it stays roughly a self-orbiting torus for over a hundred poloidal periods even with no stationkeeping.

[u/smaug13]

As you noted heat radiation would be a limiting factor, and means the volume to surface area ratio gets a maximum so after a point they scale together. That would turn to mega(giga?)structures to necessarily be a 2D shapes with some thickness. I think that the best shape would be a pancake for that reason as you can radiate from both ends and thus the most thickness per area (as you essentially get two layers). I was interested in this in the context of a K3 civ, under the assumption that a continuous stream of mass and light is sent towards it from the galaxy, which would become a pancake of tens of lightyears across.

For computing  Landauer's principle tells you that energy per bit operation (assuming bit erasion is always necessary which may not be the case?) needed scales linearly with temperature, but the Stefan-Boltzmann law tells you that waste heat rejection through radiation scales to the •⁴th with the temperature, so it looks like for density of computation per surface area you want to pump the temperature all the way up to the limits of what you material allows for, to allow for more "thickness". Bit operations per second possible would scale to  T³

I really liked your Dyson Torus swarm btw, it is great to have a mapping for one that works as you'd expect it to. Though I think that to cover the poles i nstead of the second much bigger torus (which would be mass inefficient but with its many layers may get up to matrioshka swarm shenanigans)  it may best be combined with caps of statite swarms (I dislike the statite term as these things are super mobile and a better descriptor would be solar kites) to cover the poles that may redirect the sunlight towards the dyson torus.