༄ GRAVITY ࿐

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Publicado 2024-08-02
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: physics.stackexchange.com/questions/518459/are-the…
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.gg/EMmFwEgnTz

Huge thanks to 6884 for providing the background music! Check out the album "Refactored Ontologies" here:
fallenmetropolis.bandcamp.com/album/fam127-refacto…
Songs used were "Being Not Being Not Not Being" and "Monkey On The Rocks".

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

Also, check out this viewer-made interactive web version here! observablehq.com/@rreusser/magnetic-pendulum

Todos los comentarios (21)
  • @6884
    So proud to be part of this :)
  • @suop1234
    youtube compression really doing a number on this one
  • @sorin_markov
    Me, knowing nothing about rendering and little about physics: hmmm, pretty light show
  • @theloganator13
    "I learned some CUDA" My guy, do not sell yourself short. I can only imagine the kind of parallel processing it took to get images at that resolution animating like that. This is super impressive work, and you should be really proud of it! Definitely earned a sub from me.
  • @cartermurphy1618
    saw this in my sub box and was like WHAT?? ISNT THIS THE CONNECT FOUR CHANNEL?? super cool vid though i love fractals
  • @shminge7779
    Honestly some of the best visualisations I've seen
  • HERE I WAS THINKING THIS WOULD BE A MUSIC VIDEO 😭 Unexpected math jumpscare aside, really informitive video. (The title and the tumbnail combined really makes it look like it is gonna be some crazy experimental music like Frums lol)
  • @catmacopter8545
    This reminds me of the much older video about a similarly chaotic fractal emerging when tracking where a dropped ball goes inside a circle. Very clean visuals!
  • @andjmp
    I’m familiar with fractal patterns like this based off of a magnetic pendulum model. I’ve never seen the fractals update dynamically like this before. Very cool.
  • @eeveelution8035
    Cool! I like how it looks as if it is rotating as you adjust the parameters. It's interesting to think about this as a 2D slice of a 4D state space (px, py, vx, vy where p is position and v is velocity), at vx = vy = 0. It would be cool to see a 3D slice scanning through the 4D space, you would then be able to see how the blobs of colour are all interconnected in a higher dimension.
  • @1ups_15
    youtube compression did not like that
  • @voidedbattery
    I've worked on something like this for my computer science class once! Everyone had to draw a fractal, and I decided to come up with one involving gravity just like yours. Each pixel would represent a specific point's velocity/position around a singularity. I've played around with the configuration and got some pretty cool results; I either get a comet trail or a tie dye mess. I submitted a few photos on an assignment and got bonus points from my teacher!
  • @haugenmitch
    This reminds me of the Japanese art of suminagashi. So beautiful!
  • @Miaumiau3333
    Great video! 2:55 afaik this is usually formalized by establishing a topology in the space of trajectories, where two trajectories belong to the same "region" if and only if one can be continuously transformed into the other while avoiding "bad" configurations (e.g. critical points or degenerate states)
  • @ryangrogan6839
    For the disjointed colors: A particle within a disjointed color must fall into the gravitational pull of the point who's color completely surrounds the disjointed color. I believe this is due to the fact that a particle, in order to reach its destination, must move through or close to areas where the encompassing color has strong forces. There is no way for the particle to get to its destination without doing so, which is evident by the coloration. I believe that this only holds true for properly disjointed colors (one color being entirely surrounded by on other color) Edit: I noticed a more generalized relation. The colored regions in which the path goes through shows you what points the particle will orbit during its journey. If the path only crosses into two different colors, it will only orbit those points. I'm not completely sure, but it looks like the path also somewhat defines the order in which the particle will orbit the colored points.
  • @erez2417
    literally the coolest thing ive ever seen ill be waiting for someone to add a physical background to this video one day
  • @4ntizero
    awesome design for the visuals, audio, and everything!!
  • @copywright5635
    Woahhhhhh, never heard of swap tube before. Thanks for introducing me to it! I'm definitely going to try to implement this into my future videos (especially if I end up trying to learn CUDA). Great video btw :)