༄ GRAVITY BASINS ࿐

ERRATUM:
Using numerical methods for numerical integration of the standard equation for gravitational force (1/r^2), you'll observe particles being slingshotted way out of the gravity well of the entire system, as they have the ability to "clip into" a spot deep in the 1/r^2 curve for a single timestep, and thus be accelerated enormously. Therefore, this video was rendered using the force equation f=1/(r^2+epsilon). I expected that the epsilon I chose was sufficiently small that it wouldn't change the diagrams, but that seems not to be the case. Most notably, in the 2-planet case, it turns out that with no such epsilon term, you should expect to get two perfect half-plane attraction basins. I was able to replicate that result, but timestep had to be decreased way below the range of practicality to avoid slingshotting-induced noise in the graph :/
More details here: https://physics.stackexchange.com/que...
Big thanks to commenter @imnotarobot6927 for noticing the discrepancy :)

I learned some CUDA and I wanted to show it off :D

The next connect 4 video will be a bit of a technical challenge, and I've got a lot of work left to go. So you get some "filler episodes" for the time being ;)

If you liked this video, you will definitely like my Discord server where we talk about math, programming, abstract strategy, puzzling, and so on!
  / discord  

Huge thanks to 6884 for providing the background music! Check out the album "Refactored Ontologies" here:
https://fallenmetropolis.bandcamp.com...
Songs used were "Being Not Being Not Not Being" and "Monkey On The Rocks".

Video rendered with SwapTube: https://github.com/2swap/swaptube

Also, check out this viewer-made interactive web version here! https://observablehq.com/@rreusser/ma...