@@9WEAVER9 It displays the same for everyone. Even with enhanced bitrate from premium, you cannot tell me with a straight face that moments like 1:32-1:34 display without horrible compression
If you're interested in learning more, I recommend a 2017 paper on this topic: "Slim Fractals: The Geometry of Doubly Transient Chaos" It's available for free on arxiv from a quick web search. I found it very accessible as a non-mathematician.
Me, knowing quite a bit about physics and a little about rendering: hmmm, pretty light show Don't worry it's like seeing fan service in a movie, it's nice and you appreciate it a bit more but at the end of the day I was like dayuuumm that sure looks like nice liquid paint, those colors look nice together, it's so liquidy.
"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.
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)
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!
@@Monkeymario. It makes sense, since both falling under gravity and using newton's algorithm to iterate towards minima are gradient descent algorithms at their core. Given a potential field and three potential wells, the well that an object at (x,y) ends up in might be nontrivial for all such processes
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.
I wonder is there a way to somehow mitigate youtube compression artifacts? (other than hacking into youtube using better video encoding settings or just using a ai video enhancer extension) Like maybe using some post processing effects like sharpening.
@@Monkeymario. it's impossible, youtube's compression is limited to a certain bitrate (the higher the bitrate, the better the quality), and there's absolutely no way to go above it. the only way to bypass youtube's compression is to upload somewhere else
@@twoswap you could render your original project file in 4K 60fps (even if your project is in 1080p 30fps) and upload it to youtube. The platform will allow higher bandwith at higher resolutions, I'm pretty sure this would look 2x better if you uploaded it at 4K 60fps
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.
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)
darn, I was hoping that there was a way to prove it without relying on any geometrical knowledge of the system - but if im reading you right, that is indeed needed?
@@twoswap Yep, but I think this can provide a nice rule of thumb. If you want to know whether two points belong to the same region, you have to check if you can continuously transform one point's trajectory into the other's trajectory. I think this can only be done if both trajectories wind around the stationary bodies in the same direction, because if not, then you cannot continuously transform one into the other without intersecting the stationary bodies ("bad" configurations). There is probably more nuance to this though. If you want to do this formally, you usually need homotopies.
Yeah the increase in uncertainty resulted in that wave form earlier in the video, almost perfectly matched electon probability waves. possibly multiple different subatomic models being represented here accidentally
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!
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 :)
hehe, glad you liked it! Its just my custom tool for making videos. It will probably be hard to use cause I have not spent any time other-people-proofing it yet.
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.
This is great! Amazing how complex its already in 2D, and then 3D gets on another level. Imagine trying to calculate this stuff in real time with all the stuff flying around in our solar system.
The most basic principle of electron orbitals and gravity wells are the same. Objects attract each other, in one case it's charge what attracts each other, and in the other it's the mass of the objects.
Never seen a 3d iteration of this concept, very cool!! The BGM and the nice pacing of the video was giving Posy vibes and I strive for content like that Though this is a lot different with exploring a simulation and its parameters, and I can't wait to see more Keep it up!
SOOOOO UNDERATED this reminds me of newton fractal! But it looks even cooler than newton fractal! I want an interactive gravity fractal! Here before this blows up!
I signed up for a YT premium trial to see how much the "enhanced bitrate" option would improve the quality of this video. Also, videos like this are my absolute favorite part of YT. They really motivate me to do similar things, as I am a software engineer and really like fractals, patterns, etc.
@@twoswap Oh yeah, the enhanced bitrate definitely made a noticeable difference. It's definitely not lossless quality, but still a massive improvement. Generally, this isn't an issue for me unless the video is super noisy / chaotic like this one.
One idea is instead of drag have the planets be of finite size and the particle stops when it collides with a planet. Not all starting points will end up hitting a planet though.
I started with that! It turned out generating a bunch of discontinuous visual artifacts. They were also present on a bunch of other videos on the same topic, so that seems like a common approach. But i dont like the effects it creates :p
@@twoswap I've made a lot of gravity sims myself, some other ideas that I've found interesting are rounding the direction of each particles velocity to a certain increment, for example making it so that each particle can only travel in the four cardinal directions. Also making the force of gravity the same at every distance or having planets with negative mass.
this is soooo coooooool!!!!! also yea wow this really do be the connect 4 channel. Great to see you picking up new skills and applying them to such astounding results
Absolutely one of the best videos I've seen on youtube. This kind of wonder is exactly why I love math. Beautiful and really interesting stuff, man. Great work
from the title i thought this would be a random underground soundcloud album cus sometimes i get those in my recommended. this works very well too, great work
Very cool simulations! Love the extent to which a higher emergent dimension can be visualized actively changing based on the initial parameters varying. I'll check out the website you mentioned in the description. Would be interested in checking out the code and maybe looking at the Discord.
I thought it was some kind of clickbait, I clicked expecting frustration. But it turns out that we have here a good representation of the complexity of gravity. Like
I predict a bright future in youtube for you if you keep up this high quality work. Maybe not the oddly focused connect 4 content but this animated physics stuff.
Awesome video man, can only imagine the time that went into making these visualisations as smooth as possible. Having done some 3 body simulations in the past I know how frustrating it can be to get working, so it's insane to me you have such complex systems behaving so naturally here!
I'm not going to sit here and pretend I'm able to digest this in it's entirety, but this is an INSANELY beautiful way of visualizing gravity and orbital transfers. ...when can we expect a Kerbal Space Program plugin?(:
This is fantastic! I’ve messed around a lot with Newton fractals and their idea of basins of attraction, never have I thought about doing the same but with gravity, utterly genius!
He didn't really get into any interesting details on the chaos theory or programming fronts. There's a lot better resources out there than this sort of video which is just like: oo look pretty colors but without any artistic direction
Lawful neutral Anyways this is so cool ❤ such an interesting watch Im studying physics and would like to mention but does this simulation incorporate the Moire effect as precision decreases? What inspired you to make this?
Is it my birthday? Cause the algorithm gave me a gift today. It's been 18 hours since you posted this and you're at 1100 views. Congrats in advance for the 1M views you're about to get. Excellent work!
amazing video. i have always loved physics and gravity sims especially - id be interested in a video about how you actually were able to render these simulations
So proud to be part of this :)
hell yeah man, the tunes are great :) appreciate it again!!
i swear ive seen that profile pic somewhere before
also you only have 4 subs?! WHAT
Sick music
Would be awesome for you both to get together to have a dedicated music video remaster using this visualization (and any others you can think of)
youtube compression really doing a number on this one
Fr
man i was gonna comment that >:(
was fine for meee
@@9WEAVER9 It displays the same for everyone. Even with enhanced bitrate from premium, you cannot tell me with a straight face that moments like 1:32-1:34 display without horrible compression
it doesn't matter if you watch this in 144p 😅
holy album art generator
lol, what should my band name be
@@twoswap n-body problem, where n is the number of band members
beautiful
The Fractal 5
@@twoswapbeautiful
Me, knowing nothing about rendering and little about physics: hmmm, pretty light show
Fr
Ooga booga funny colors
If you're interested in learning more, I recommend a 2017 paper on this topic:
"Slim Fractals: The Geometry of Doubly Transient Chaos"
It's available for free on arxiv from a quick web search.
I found it very accessible as a non-mathematician.
Me, knowing quite a bit about physics and a little about rendering: hmmm, pretty light show
Don't worry it's like seeing fan service in a movie, it's nice and you appreciate it a bit more but at the end of the day I was like dayuuumm that sure looks like nice liquid paint, those colors look nice together, it's so liquidy.
Frfr
"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.
Everyone is admiring how beautiful it looks but no one else is admiring how much work he put in!
Thank youu 😭😭🙏 im glad you liked it :)
Incredible video. A masterpiece.
i love cuda so much lol
@@Monkeymario.Few people would understand. I certainly don't. Only aware from these sorts of comments 🙏
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)
nothing too crazy this time but it might get crazier in the following, why not...
I THOUGHT THE SAME😭😭
Omg imagine this w frums bga
@@carbonatedmilk1 True (frums is so good, no one can convince me otherwise)
BRO SAME XD
Honestly some of the best visualisations I've seen
Thanks!! :D
@@twoswap:D
saw this in my sub box and was like WHAT?? ISNT THIS THE CONNECT FOUR CHANNEL??
super cool vid though i love fractals
Thanks!! :D
what? this channel was a connect 4 channel?
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!
this reminds me of the newton fractal!
@@Monkeymario. It makes sense, since both falling under gravity and using newton's algorithm to iterate towards minima are gradient descent algorithms at their core. Given a potential field and three potential wells, the well that an object at (x,y) ends up in might be nontrivial for all such processes
ruclips.net/video/C5Jkgvw-Z6E/видео.htmlsi=uD-evpcr48EVEsXr
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.
Thanks!!
youtube compression did not like that
we do not get along
I wonder is there a way to somehow mitigate youtube compression artifacts? (other than hacking into youtube using better video encoding settings or just using a ai video enhancer extension) Like maybe using some post processing effects like sharpening.
@@Monkeymario. it's impossible, youtube's compression is limited to a certain bitrate (the higher the bitrate, the better the quality), and there's absolutely no way to go above it. the only way to bypass youtube's compression is to upload somewhere else
@@twoswap you could render your original project file in 4K 60fps (even if your project is in 1080p 30fps) and upload it to youtube. The platform will allow higher bandwith at higher resolutions, I'm pretty sure this would look 2x better if you uploaded it at 4K 60fps
@@mooooooooooooove worth a shot i guess.. if not, there's always v i m e o (cough cough), but the reach is just not the same
4:38 NOOOOOO THE THREE BODY PROBLEM WILL HAUNT ME FOREVERRRRRR
wow it's the real riley
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.
This!
THAT WOULD BE SOOOOOOOOO COOL
Love it
Just wanted to say that you've done SUPER good job on choosing the colors. As a color blind guy (protanomaly) I'm incredibly grateful! :)
Yeah I'm not color blind but the color choices are tbh very beautiful! :D
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)
darn, I was hoping that there was a way to prove it without relying on any geometrical knowledge of the system - but if im reading you right, that is indeed needed?
@@twoswap Yep, but I think this can provide a nice rule of thumb. If you want to know whether two points belong to the same region, you have to check if you can continuously transform one point's trajectory into the other's trajectory. I think this can only be done if both trajectories wind around the stationary bodies in the same direction, because if not, then you cannot continuously transform one into the other without intersecting the stationary bodies ("bad" configurations). There is probably more nuance to this though. If you want to do this formally, you usually need homotopies.
@Miaumiau3333 Thanks for explaining!!
5:56 looks like electron orbitals
I noticed that as well! I wonder how these ideas are related. Fascinating
Yeah the increase in uncertainty resulted in that wave form earlier in the video, almost perfectly matched electon probability waves. possibly multiple different subatomic models being represented here accidentally
Imagine if this RUclips video found the key to a theory of everything by linking gravity to the subatomic scale.
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!
Kudos to you
This reminds me of the Japanese art of suminagashi. So beautiful!
Woah, TIL! They definitely look similar!
@@twoswap Agree! In my opinion gravity fractals are way cooler and beautifuler!
Me when cool video from cool RUclipsr
^v^
@@twoswapcool emoticon! :D
This is one of the coolest things I've ever seen on youtube, thank you!!!!
literally the coolest thing ive ever seen
ill be waiting for someone to add a physical background to this video one day
Sound design on this video is incredible and it’s mixed perfectly
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 :)
hehe, glad you liked it! Its just my custom tool for making videos. It will probably be hard to use cause I have not spent any time other-people-proofing it yet.
swap tube? what when is that mentioned in the video OH THE DESCRIPTION
this is so immersive and beyond beautiful thank you
2:04 has to be my fav
same
Same!
I have to say, this right here might be the single best thumbnail I've ever seen. Proud to say I'm now a subscriber
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.
This is great! Amazing how complex its already in 2D, and then 3D gets on another level. Imagine trying to calculate this stuff in real time with all the stuff flying around in our solar system.
awesome design for the visuals, audio, and everything!!
Thank you!!
Agree!
this simulation will fuel the return of the screen saver
5:16 These kind of look like electron orbitals. Is that just a coincidence, or is there a reason behind it?
The most basic principle of electron orbitals and gravity wells are the same. Objects attract each other, in one case it's charge what attracts each other, and in the other it's the mass of the objects.
It almost looks like we’re trying to view a 4d shape but cant
My dude drops in. Poses a question. Shows some neat pictures. Then dips the f out. I respect it.
Clicked on this for no reason. Some of the coolest work ive seen on the platform
Never seen a 3d iteration of this concept, very cool!!
The BGM and the nice pacing of the video was giving Posy vibes and I strive for content like that
Though this is a lot different with exploring a simulation and its parameters, and I can't wait to see more
Keep it up!
Thank you!!
FINALLY
the youtube recommendation system FINALLY gives me some gold to watch!
this is genuinely amazing, I'd love to see more videos like this!
Thanks!! :D
This is actually insane and i love it (man fractals are cool)
SOOOOO UNDERATED this reminds me of newton fractal! But it looks even cooler than newton fractal! I want an interactive gravity fractal! Here before this blows up!
I signed up for a YT premium trial to see how much the "enhanced bitrate" option would improve the quality of this video.
Also, videos like this are my absolute favorite part of YT. They really motivate me to do similar things, as I am a software engineer and really like fractals, patterns, etc.
im curious how the experiment went!!
and definitely worth a try to do something similar :)
@@twoswap Oh yeah, the enhanced bitrate definitely made a noticeable difference. It's definitely not lossless quality, but still a massive improvement. Generally, this isn't an issue for me unless the video is super noisy / chaotic like this one.
These patterns would make for a really cool shirt design!
Agree!
Lol, maybe ill have to set up a redbubble shop on the side
genuinely breakthrough math, incredible work!
2:22 this part has a kinda weird 3D effect for a moment
This is such a beautiful and intuitive demonstration of chaos theory and visualization. Well done.
holy sweet mother of bitrate
this is literally magical
One idea is instead of drag have the planets be of finite size and the particle stops when it collides with a planet. Not all starting points will end up hitting a planet though.
I started with that! It turned out generating a bunch of discontinuous visual artifacts. They were also present on a bunch of other videos on the same topic, so that seems like a common approach. But i dont like the effects it creates :p
@@twoswapoh ok
@@twoswapdid you try with both finite size and drag?
yep
this is sooo cool
i love that its animated and not just static images
Incredible!
Thanks :)
The fact that you thought of this and were able to come up with, let alone write the shaders is just wild!
1:07 what a weird ball sorting system
No, it was planned to end up that way
@@Matches1st welcome to the joke
@@Koreley this joke was incredibly hard to get what in the world
@@Matches1st I'm not the best at jokes
wow I remember seeing a very old video based around this topic, but this goes much deeper! also very clean simulations/animations
I wonder how modifying the mass of individual planets effects the graph
I would love to know- thats a great question which I unfortunately didnt explore!!
@@twoswap I've made a lot of gravity sims myself, some other ideas that I've found interesting are rounding the direction of each particles velocity to a certain increment, for example making it so that each particle can only travel in the four cardinal directions. Also making the force of gravity the same at every distance or having planets with negative mass.
This is amazing. I didn't expect it at all. Really smart and artistic work.
Babby’s first three body problem
this is soooo coooooool!!!!!
also yea wow this really do be the connect 4 channel. Great to see you picking up new skills and applying them to such astounding results
wat
Thanks to RUclips for recomending me this video
Is this real chat
Chat this could be big
It's real
No
Oh the fourth-person pronoun…
@@distorted_heavyyes
This is the best video ive seen in a while! So pleasing and enlightening
Love the one at 1:50 !! Can you make it a poster ?!
the math flavored music is so beautiful man
Man I love this video and the visual representation of where each ball ends
Absolutely one of the best videos I've seen on youtube. This kind of wonder is exactly why I love math. Beautiful and really interesting stuff, man. Great work
Would be great to have 3b1b cover some chaos theory topics. He would bring a lot of mathematical rigor and educational explanations to it im sure
This is some of the most gorgeous renders I've seen since 3B1B
This was both visually and intellectually astounding!
from the title i thought this would be a random underground soundcloud album cus sometimes i get those in my recommended. this works very well too, great work
I'm in love with this. This is so good.
Very cool simulations! Love the extent to which a higher emergent dimension can be visualized actively changing based on the initial parameters varying. I'll check out the website you mentioned in the description. Would be interested in checking out the code and maybe looking at the Discord.
Now THIS looks really cool
Dude I was incredibly impressed by this
This is now my favorite procedural generated texture method, it's ridiculously satisfying
I thought it was some kind of clickbait, I clicked expecting frustration. But it turns out that we have here a good representation of the complexity of gravity.
Like
YEAAAHHH I LOVE THIS KINDA MATH
stunning work, thank you!
I'd never thought about gravity this way before. These regions are wild. Thank you!
Glad you liked it!! 😄
I predict a bright future in youtube for you if you keep up this high quality work. Maybe not the oddly focused connect 4 content but this animated physics stuff.
lol, this was supposed to be the "filler" video while I worked on more connect 4 stuff, but it seems people liked it more
@@twoswap Sorry, I don't mean to critique you interests, but I do think that this content has a far broader audience. I enjoyed it very much.
no no I dont mind I just think its funny lol
i swear i need long looped gifs of this to use as a wallpapet
Awesome video man, can only imagine the time that went into making these visualisations as smooth as possible. Having done some 3 body simulations in the past I know how frustrating it can be to get working, so it's insane to me you have such complex systems behaving so naturally here!
one of the best videos on this topic I've seen
Eh, it doesn't really cover the real details just has some nice animations
You mighty legend! This is incredible.
I came in thinking this was going to be music, and I was delighted with some cool nerd stuff. You’ve earned my trust
hey there was music too! ☜(ಠ_ಠ☜)
Impressive visualization !! Keep 'em coming!
3 body problem has been on RUclips for a long time. Never saw something that's rendered as a map. I'm glad I have been invited by the RUclips algo.
This deserved an instant subscribe. Some frames are just background worthy for me. Well done!
I'm not going to sit here and pretend I'm able to digest this in it's entirety, but this is an INSANELY beautiful way of visualizing gravity and orbital transfers.
...when can we expect a Kerbal Space Program plugin?(:
What I find absolutely nuts is that this is natural! It's a natural phenomenon! And it's algorithmic in nature!
Holy shi this looks so beautiful
This was all i hoped to see and so much more
Music and commentary are a perfect compliment to the concept
Thanks!!
also thanks!! :)
Truly beautiful and underrated video, can't wait till the algorithm picks this one up more
This is beautiful.
Thank you!!!
This is fantastic! I’ve messed around a lot with Newton fractals and their idea of basins of attraction, never have I thought about doing the same but with gravity, utterly genius!
thank you!!!
This BLEW my mind
He didn't really get into any interesting details on the chaos theory or programming fronts.
There's a lot better resources out there than this sort of video which is just like: oo look pretty colors but without any artistic direction
Try the 2017 paper: "Slim Fractals: The Geometry of Doubly Transient Chaos"
Lawful neutral
Anyways this is so cool ❤ such an interesting watch
Im studying physics and would like to mention but does this simulation incorporate the Moire effect as precision decreases?
What inspired you to make this?
Is it my birthday? Cause the algorithm gave me a gift today.
It's been 18 hours since you posted this and you're at 1100 views. Congrats in advance for the 1M views you're about to get.
Excellent work!
hehe we'll see!! glad you liked it :D
this is the best random yt vid ive seen in a while
amazing video. i have always loved physics and gravity sims especially - id be interested in a video about how you actually were able to render these simulations
I really enjoyed this video. Thank you!
This must have taken so much time to render! Awesome dude
it sure did 😭😭 glad you liked it!!