You can run this kind of simulation on any PC because they are not run in real time. It can take few seconds per frame to render. But once every frames are generated, you just pile them at 30fps
@@john_hatten2862 if you wanted you could literally run this simulation by doing the math yourself for each frame. It’d take fucking forever, but you could.
@@connorcriss oh man I can't imagine how precise you must be to make it work. If you round at 0.000000000000001 (assuming the pendulum lenght is 1), you would still get completely different results after few seconds
It's like... the closer together they are in angle, the longer they stay seemingly in sync, and yet the more vehemently they separate once they fall out of it
@@joshuahudson2170 The simulation is correct for a double pendulum system made of two point masses (the rod connections are massless, thus being impossible to replicate in the real world). These systems are easier to solve then a real double pendulum that has mass associated with the rod connection, not just the pivot and end point. Regardless, double pendulum systems are great examples of chaotic motion and it is hard to guess how they will behave without solving the system as is shown. The most interesting part of these systems is that one may find some initial conditions that, even after a very long time t, the masses of the pendulum have not entered one or more bounded regions. These regions are usually vertically symmetric. You could have some double pendulums swing for all time, assuming no external resistance or damping, and still have neither mass ever enter a particular region, while knowing this region is defined by your initial conditions somehow. We just don't have a functional form defining that area from starting conditions due to the nature of chaotic motion. Since we know classical mechanics, which describes this interaction, is deterministic, a functional form should exist but we have yet to derive it and are stuck having to solve, across t, a two point mass system.
Me: WHY does TH-cam constantly keep recommending me random double-pendulum videos? I don't really care about this besides as a mathematical curiosity Also Me: *clicks on and watches every recommended double-pendulum video*
Have you ever truly experienced the k-hole where your mind disassociates from your body and reality? Have you ever experienced the feeling of your mind searching for reality while no longer being certain that it exists or what it is?
@@Bob13454 The spread of those pendulums would only happen for different lengths. If they are all identical, they will all follow the exact same path and no pattern will be produced
If you do think about this as the butterfly effect, then it’s pretty cool to see that radically different outcomes *do* intersect sometimes. Kind of proves you should never give up.
I'm sorry to say but that is not true. They may intersect in real space but if they do, then not in momentum space. That is to say, the pendulums do have a different velocity when they are at the same place. And for future reference the velocity is just as important as the location.
The butterfly effect, when referring to double pendulums, is not the same as the popculture butterfly effect in relation to space-time. While both relate to their field in the same way, they don't exactly represent the same thing. The butterfly effect here is referring to the Chaos Theory definition of the butterfly effect: A miniscule change in a chaotic deterministic nonlinear system causes radical changes later in the system. The pendulums aren't actually interacting with each other. Our creator simply programmed each pendulum to travel an additional 0.01 radians farther from the next. That's why, despite such a small change from each state, the result is exceptionally different.
We definitely need more of double pendulums, and most certainly a separate extended music video. This was absolutely amazing. Can't come up with words to describe how this made me feel. Unbelievable.
The way it goes from a single line to unimaginable complexity, I wonder if it played for enough time it would return again to a single line. Drawing some parallels with what I’ve desperately tried to discern from several potent DMT trips.
It looks like the limited floating point precision is showing up as grouping of the pendulums just as they break apart. Would be cool to see the same run with higher / lower precision side by side.
Not sure where you're seeing that? Would be interesting to know what type of data structure @AssortedContent used though. x86-64 supports 80 bit floating points in hardware, I think that's the highest precision you can get with a standard CPU. It has 64 bits of precision for the significand. I would imagine, but might be wrong, that that would be enough for a simulation? If not of course you can go arbitrarily higher, you just lose acceleration so it takes a lot longer.
i agree that some artifact must be causing this. if one checks out the video linked in the video description, there is a 500 double pendulum one. despite much fewer number of pendulums, the way way those pendulums spread apart is visually much more elegant compared to how the spreading in this video starts off much more randomly and erratically.
@@lost4468yt 80 bit floats are used in registers, but in memory they are whatever precision you store them as. Here it was 32bit, which probably wasn't enough imho.
I love how you can (basically) point at the moment that the system transitions to chaos. This is particularly true of the later examples where initial conditions are quite close. I wonder if generalizations can be made about the ways in which this phase transition occurs. Another very interesting video is "Space-Time Dynamics in Video Feedback" from 1984. Equal parts art and science.
I like to imagine the edge of the pendulum to be the point where things become statistically impossible. What i like about this allegory is that in real life, one of the million pendulums will eventually break and fly of this metaphorical circle of probability and make the impossible happen.
Try checking some different synth wave compilations- dark ambient, retro, etc. That's the closest I can think of to this sound. I do agree that the track for this video is good. It reminds me of some of the 1980's 4AD alt stuff, but with the dance beat removed.
It's like watching the quantum possibilities of the pendulum. I think that if we could see reality in higher dimension would look like this but from our perpective the wave (which are the possibilities) becomes the particle (one possibility perceived only).
I feel like these presentations is one big metaphor for life. You start out simple, orderly, and ready for your next thing to do, then when you're an adult, your life devolves into utter chaos where there is no order and you don't know what to do.
The most impressive thing is that there are visible gaps. This means the difference of 2 of these million pendulums are still so far appart that it creates visible gaps. Damn. (Or it's weird clustering)
It seems like “unfolding” events are when the most chaos is introduced There are kind of two types, which I will call Rotary unfolding and Linear unfolding Rotary unfolding is when the upper pendulum swings not quite a full way to pointing up, but stops short and the secondary pendulum swings a full circle The second type of unfolding, linear unfolding, is when the two pendulums face opposite directions, so the tip of the second pendulum passes through the beginning of the first, and it takes varying time for it to leave that position, and different directions and speeds it can leave at, causing it to split into a variety of discreet groups which can later break apart
i want to see better screensavers like the start of each segment of the showcasing of the pendulums swinging, but the smoothness and spectrum kinda thing just keeps going
![จบจนได้ ! | Black Myth: Wukong #007 [ตอนจบ?]](http://i.ytimg.com/vi/DSqvWndF0sw/mqdefault.jpg)
![[UNCUT] The Loyal Pin ปิ่นภักดิ์ EP.4 (4/4)](http://i.ytimg.com/vi/d3l5rxl5CVo/mqdefault.jpg)
So this is what your blanket looks like to you at 3am, trying to find the long side.
Accurate
Omg relatable
Oh my god
imagine not finding the long side when you have night vision
and also flipping it to the smooth side
What my elbow feels like after hitting it on the table
elbow be like :AÆÂĒīā
I was just gonna comment that lol
I recently broke my elbow and can tell you: hitting it on the table hurts more.
But the pain goes away much, much faster.
cool pfp
0:52
the legend wrote this in rust, made their own renderer for it AND made their own music for it. what a legend
Only true chads know how you knew ;)
Not to be that one guy, but they used SFML which is based on OpenGL and is it’s own renderer. While impressive, they didn’t make the renderer
shut up nerds
@@blazeytown4444 ok............... :(
@@whigmalwhim4760 nope. I piped pixels into ffmpeg
0:47 the way the music synced here was probably the most satisfying thing I’ve seen all week
Hello, fellow Will
That was intentional :p
@@AccentedContent lol
@@AccentedContent awesome stuff
Absolutely, I love it
The 1mil version stopped way too soon, I would have liked to watch it a little longer after things went chaotic.
it probably took hours to rendet
@@incription yea rendering this many of them can take hours or even days depending on what GPU you have.
the first one was a million
@@SpectreDev You can render this many in real time with gpu computing, not that big of a deal
@@mymo_in_Bb Lmao it started with 1 000 000 then 100 000 then 10 000
Waiter: Here’s your check.
Me: You too.
Also my brain:
hands waiter a bill
cheque :)
Check mate
I can only imagine how powerful your pc has to be to load that kind of thing. Give this man some subs, he/she deserves it
You can run this kind of simulation on any PC because they are not run in real time. It can take few seconds per frame to render. But once every frames are generated, you just pile them at 30fps
@@john_hatten2862 if you wanted you could literally run this simulation by doing the math yourself for each frame. It’d take fucking forever, but you could.
@@connorcriss oh man I can't imagine how precise you must be to make it work. If you round at 0.000000000000001 (assuming the pendulum lenght is 1), you would still get completely different results after few seconds
"give this man"
"he/she"
hmmm
@@Konomi_io nobody asked
It's like... the closer together they are in angle, the longer they stay seemingly in sync, and yet the more vehemently they separate once they fall out of it
quantum mechanics at its finest
@@NFITC1 This is purely classical mechanics, nothing quantum about it.
I'm wondering if it's a simulation limit.
@@joshuahudson2170 The simulation is correct for a double pendulum system made of two point masses (the rod connections are massless, thus being impossible to replicate in the real world). These systems are easier to solve then a real double pendulum that has mass associated with the rod connection, not just the pivot and end point. Regardless, double pendulum systems are great examples of chaotic motion and it is hard to guess how they will behave without solving the system as is shown. The most interesting part of these systems is that one may find some initial conditions that, even after a very long time t, the masses of the pendulum have not entered one or more bounded regions. These regions are usually vertically symmetric. You could have some double pendulums swing for all time, assuming no external resistance or damping, and still have neither mass ever enter a particular region, while knowing this region is defined by your initial conditions somehow. We just don't have a functional form defining that area from starting conditions due to the nature of chaotic motion. Since we know classical mechanics, which describes this interaction, is deterministic, a functional form should exist but we have yet to derive it and are stuck having to solve, across t, a two point mass system.
@@NFITC1 quantum is in reference to something at the atomic level. you used it incorrectly in this statement
This would be one hell of a computer background
I think you're thinking about...screen_Saver
@@iSyriux No, desktop backgrounds are NOT called screensavers.
true
Me: WHY does TH-cam constantly keep recommending me random double-pendulum videos? I don't really care about this besides as a mathematical curiosity
Also Me: *clicks on and watches every recommended double-pendulum video*
The algorithm is a beast that must be fed. Thank you for your contribution.
The more 0's after the decimal, the more I'm tripping on katamine.
...meow?
1.
@@6884 fax
Have you ever truly experienced the k-hole where your mind disassociates from your body and reality? Have you ever experienced the feeling of your mind searching for reality while no longer being certain that it exists or what it is?
@@acarpentersson8271 *EVERYDAY*
You can't just get me addicted to a video this short.
Yep, we need a longer 1 million one, possibly slower so the change is more gradual? That was mesmerizing!
Ngl it’s so cool how all these pendulums start in almost the same location and go the same way and yet end up totally different
Almost like physics isn't real...
@@andreiandrofski9426 ?
@@Bob13454 The spread of those pendulums would only happen for different lengths. If they are all identical, they will all follow the exact same path and no pattern will be produced
@@andreiandrofski9426 It says in the video the starting angles are very slightly different.
@@Bob13454womp womp
This is beautiful i have looked at it for five hours
I don't know how but this helped me emotionally, which i was looking for. So, thank you 🦋
That split at 1:11 was so cool to see!
That music was beautiful and I would love to listen to a full version. It was existential man.
If you do think about this as the butterfly effect, then it’s pretty cool to see that radically different outcomes *do* intersect sometimes. Kind of proves you should never give up.
That was... Exactly what I needed to hear. Thank you
But…4D
I'm sorry to say but that is not true. They may intersect in real space but if they do, then not in momentum space. That is to say, the pendulums do have a different velocity when they are at the same place. And for future reference the velocity is just as important as the location.
The butterfly effect, when referring to double pendulums, is not the same as the popculture butterfly effect in relation to space-time. While both relate to their field in the same way, they don't exactly represent the same thing. The butterfly effect here is referring to the Chaos Theory definition of the butterfly effect: A miniscule change in a chaotic deterministic nonlinear system causes radical changes later in the system.
The pendulums aren't actually interacting with each other. Our creator simply programmed each pendulum to travel an additional 0.01 radians farther from the next. That's why, despite such a small change from each state, the result is exceptionally different.
@@XoIoRouge r/iamverysmart
0:30 BEAUTIFUL
We definitely need more of double pendulums, and most certainly a separate extended music video. This was absolutely amazing. Can't come up with words to describe how this made me feel. Unbelievable.
Rendering is as amazing as music...both are epic creations 🔥
This is EXACTLY the content I want to watch late at night!
This is one of the most beautiful things on the internet
You can almost see a perfect circle in the middle of all the chaos and that's beautiful
Yeah I mean with that many instances, pure chance would have drawn you a circle as well.
I love how all of these slowly greet you before desceneing to chaos
The way it goes from a single line to unimaginable complexity, I wonder if it played for enough time it would return again to a single line.
Drawing some parallels with what I’ve desperately tried to discern from several potent DMT trips.
in theory yes, but it would take longer than the age of the universe for it to happen.
It looks like the limited floating point precision is showing up as grouping of the pendulums just as they break apart. Would be cool to see the same run with higher / lower precision side by side.
Not sure where you're seeing that? Would be interesting to know what type of data structure @AssortedContent used though. x86-64 supports 80 bit floating points in hardware, I think that's the highest precision you can get with a standard CPU. It has 64 bits of precision for the significand. I would imagine, but might be wrong, that that would be enough for a simulation? If not of course you can go arbitrarily higher, you just lose acceleration so it takes a lot longer.
the pendulums break apart because there is a finite amount of them
@@awesum8r882 still looks like there's only a few hundred of them
i agree that some artifact must be causing this. if one checks out the video linked in the video description, there is a 500 double pendulum one. despite much fewer number of pendulums, the way way those pendulums spread apart is visually much more elegant compared to how the spreading in this video starts off much more randomly and erratically.
@@lost4468yt 80 bit floats are used in registers, but in memory they are whatever precision you store them as. Here it was 32bit, which probably wasn't enough imho.
I love how you can (basically) point at the moment that the system transitions to chaos. This is particularly true of the later examples where initial conditions are quite close. I wonder if generalizations can be made about the ways in which this phase transition occurs. Another very interesting video is "Space-Time Dynamics in Video Feedback" from 1984. Equal parts art and science.
0:48 this timing is sick
THE EMPEROR OF LIGHT
What does that mean?
@@AccentedContent could be a reference to terrarias boss empress of light
Yup
Fire soundtrack my man
Can we just take a moment to imagine the art that could be if each penglulem was tracing there paths with different colors each?
Make it!
Thanks for making this awesome song! Im crediting you for my extension of this!
This has a lot of desktop wallpaper potential.
I think my video has helped yours grow a bit in the last week or so, thanks for the inspiration!
He’s using the matrix to render all this
Idek what I just watched but it was nice. The music made it a bit tense but the colors just washed that away. Very nice.
The sync at 0:35, is amazing, pls release a full song of this.
I like to imagine the edge of the pendulum to be the point where things become statistically impossible. What i like about this allegory is that in real life, one of the million pendulums will eventually break and fly of this metaphorical circle of probability and make the impossible happen.
nobody:
companies during pride month: 0:06
I need to watch this while high someday
How long did this take to render?
1M took like an hour cause I didn't parallelize it. Maybe next time
I just set both this comment and the following reply to 69 likes.
@@extrapathos >:)
i love how quickly it goes from "that looks kinda cool" to "eldrich abomination"
Thx for being 420
You made the music for this? Could listen to a whole album of it! Really like the sound
Me too
Try checking some different synth wave compilations- dark ambient, retro, etc. That's the closest I can think of to this sound. I do agree that the track for this video is good. It reminds me of some of the 1980's 4AD alt stuff, but with the dance beat removed.
Agreed
It's like watching the quantum possibilities of the pendulum. I think that if we could see reality in higher dimension would look like this but from our perpective the wave (which are the possibilities) becomes the particle (one possibility perceived only).
Idk 1:17 looks kinda german
Reaching
I feel like these presentations is one big metaphor for life.
You start out simple, orderly, and ready for your next thing to do, then when you're an adult, your life devolves into utter chaos where there is no order and you don't know what to do.
Alright who yelled Siri?
We went from a bendy stick to a cool rainbow to *utter madness*
video 17 of travelling across the internet:
holy shit this looks cool
This actually sort of shows how at the start, double pendulums are actually sort of predictable, but it kind of goes a bit crazy afterwards.
TH-cam compression be like: HELP I CAN'T HOLD THIS ANYMORE
This is such a clear depiction of the essence of chaotic systems... thank you for the animation
The most impressive thing is that there are visible gaps. This means the difference of 2 of these million pendulums are still so far appart that it creates visible gaps. Damn.
(Or it's weird clustering)
The chaos of nature is so beautiful
Please put this music on spotify
This, or like a sound cloud or something.
It's same music as the soundtrack of the movie "Predestination"
@@sagittarius284 which song in the soundtrack tho
i wish someone would make a video like this, but the double pendulums would stay together as a rainbow and keep the beauty intact
0:44
1:12 A sudden bifurcation. I guess the phase portrait might look special at that point.
0:45 the timing with the music is EPIC
i feel like there must be some way to mathematically simulate infinite pendulums, so its always smooth no matter how long you go
The fact that such an absolutely minuscule difference in position can cause such a huge difference is kinda scary
Chaos is our limited interpretation of a portion of pattern and order ultimately leading to entropy and equilibrium
Interdimentinal Skittles....
Get hypnotized by the rainbow.
I just love how the circle is established and maintained amidst the wonderful "butterfly wings"...So cool😘😘😘😘😍
The beat drop at 0:47 was so well placed
Music for these type of videos are always good
oh wow they end up roughly taking the shape of cardioids!!! that’s so cool :0
That music was fantastic accompanying the model
So much complexity from such a simple rules.
clicked for the million, stayed for the ten thousand
These things are mesmerizingly beautiful
0:47 and 0:51 the way it lined up with the music was so nice
It seems like “unfolding” events are when the most chaos is introduced
There are kind of two types, which I will call Rotary unfolding and Linear unfolding
Rotary unfolding is when the upper pendulum swings not quite a full way to pointing up, but stops short and the secondary pendulum swings a full circle
The second type of unfolding, linear unfolding, is when the two pendulums face opposite directions, so the tip of the second pendulum passes through the beginning of the first, and it takes varying time for it to leave that position, and different directions and speeds it can leave at, causing it to split into a variety of discreet groups which can later break apart
Chaos is so beautiful.
i want to see better screensavers like the start of each segment of the showcasing of the pendulums swinging, but the smoothness and spectrum kinda thing just keeps going
I have no idea about what is this, but I'm pleased to see this being recommended to me.
I would like this on my computer lock screen!
people who try to separate math and art are fools because this is a wonderful crossover
It's like every iteration is a probable outcome, like we are seeing what a multiverse event looks like
Great, crisp quality
Music made it even cooler!
It's just amazing. We are all living different lives but all have the same origin. And end. It's one and all at the same time.
I feel like if we wait long enough all million pendulums will reach the same position
The more you want to keep things together, the more it will change after a single event horizon.
my phone lagged just watching this
the music makes me think like there's some sort of cosmic horror always watching
The more I watch chaos geometry, the less chaotic it all becomes and unexpectedly familiar just as any other common input
I really have the sensation of having seen this on tv before when I was little, I don't know why...however, this is so cool
It looks like 4D piece of cloth.
You can see how it moves, you can feel that it's like cloth, but you don't know where are the edges of it.
Nice visuals !
God particle is hiding in the top of the 'circle' ;)
I find it very interesting that changing one little thing can change everything
I found this on my recommendations and idk how it got there but I like it!
Someone needs to tell this guy the correct definition of butterfly effect
This video and audio is gorgeous
Seeing the universe unravel before your eyes is quite marvelous
Congratulations! You just created a new BBC ident
Like the best oldschool screensaver ever
1 million and it still didn't cover all the possibilities! Amazing