Are there other Chaotic Attractors?
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- Опубліковано 6 лют 2025
- A showcase of chaotic dynamical systems, similar to the Lorenz Attractor, coded in C++ and SFML.
Github: github.com/xMi...
Mathstodon: mathstodon.xyz...
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Equations: www.3d-meier.de...
Music: La Cathédrale Engloutie - Claude Debussy
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Thanks for watching, leave a like and share with your friends.
this is amazing. these attractor graphics with a higher framerate and longer runtime and you've got the perfect screensaver ngl
Made a program like this in Processing a while ago, used it as my live wallpaper on Android. Could definitely be done on PC
@@EggKiddo I never knew you could use processing to create live wallpapers 😯
I'm going to actually dive into it this time!
How about you just take the equations (or approximations of them that require less computing power) and run them as a particle system in real time?
Then you get a unique wallpaper everytime!
@@EggKiddo Please share it! I'd absolutely love to see them! I dont have a coding background otherwise I'd do it myself haha
@@rpyrat There is an app called APDE which can export your sketches as a live wallpaper
I think I just found my senior thesis topic. Thank you so much.
Edit: My Senior Thesis was on the Lorenz Attractor. My professors gave me an A! Thank you for the inspiration!!!!
Congratulations! That's so amazing!
CONGRATS STRANGER THATS CRAZY 🥳
'A' is for attractor!
@@orfeasliossatos welp the comment is kind of late
@@egebabus3423better late than never
It’s amazing how each Attractor never fails to appear harmonic and synchronised
Chaotic Composers, Everything is music, art, creativity, same thing but different initial inputs and expressionism different output.
This is a beautiful video, and I think the choice of Debussy is befitting.
Always finish on de Bach, never on Debussy.
Family guy
The Debussy fits so perfectly
@@benjamintoulouse7052 weirdly specific but kinda relatable at the same time
@@alexanderbayramov2626 relatable pfp to insert into this comment chain de Bach
what is debussy?
Bruh I come from a math HS and my skills are so lacking yet "existing" enough to grasp a very tiny bit of this, thanks for reminding me I've gotta study more and more and more given how beautiful what awaits me could be 👀✨❤️
these are all little systems of PDEs
I'm really glad you liked it, stay curious my friend!
I just finished an applied math PhD and if I could go back and talk to myself in high school, I'd say "there's so much more beautiful math that you can't even begin to imagine.."
@@complexobjects sure gives a lot to look out for thanks man!! :D
@@complexobjects I've yet to encounter math that is beyond me, could you cite an example so I can push myself?
very thoughtful music choice that added a lot of depth to the video. Debussy's pieces often "chaotically attract" around different tonal centers, and unpredictably. With a sense of delicacy and intentional grace and symmetry. I appreciate Debussy for very similar reasons the chaotic attractor visualizations are so interesting to look at
I enjoyed hearing a less familiar Debussy piece! Gymnopedie and the arabesques are lovely but this one was a surprising gem!
@@mikeciul8599 All of Debussy is stunningly captivating and beautiful! and gymnopedie is actually Satie :) Check out Valse Romantique from Debussy for an interesting sort of Satie-inspired sound mixed with beautiful Debussy harmony
DE WHAT
@@marselo1316 lmaooooooooooooooooooooo
@@marselo1316 you can't call yourself a man if you don't like debussy...
there’s something so philosophical to this kind of math, it’s so mystical in its abstractions whenever you derive some sort of physical idea from it, it feels so much better than just saying it.
Been sitting in matlab all day staring at such black dots flying around trying to understand a system. This was quite a bit more entertaining!!
what are you working on if you don't mind me asking?
@@alexandramuller9055 Hi, sure! I don't know how familiar you are with maths but - it was just a university assignment regarding dynamical networks where each node represented an oscillating complex number and there was diffusion in the network so eventually nodes would synchronize if the system was stable and attain the same real and complex parts. The value of each node was described by and ODE with a forcing term causing oscillations and a diffusion term including differences between the current node and each of its neighbouring nodes. In the images in this video synchronisation is happening when alll the dots converge to the same point and move together! This happens mathematically when the diffusion difference term in each ODE equals 0, hence all nodes have the same value! Tell me if you don't understand anything and I could simplify haha :)
@@cha4kn whats diffusion?
@@Dabnaait is generally speaking the process of some quantity spreading from a region of high concentration to a region of less concentration. Such occurs everywhere at all times, and includes things as liquids, gasses and even humans. So, seeing the value of a node in my example as a value of concentration, or density, diffusion will raise the value of neighbouring nodes if a node has a high value.
@@cha4kn wow, thanks, that's really interesting stuff
the music fits beautifully with the movements... simply beautiful!
Anyone who uses Debussy to set the mood for complex beautiful animations gets my upvote automatically.
Debussy??? 🤨🤨🤨😳😳
Ah, math fireworks. Every day can be the 4th of July when you love math.
love this comment!
Hi again!
I noticed that a lot of people recognized and enjoyed Debussy's "La Cathédrale Engloutie". I just wanted to let you know that besides studying data science, I'm also a cellist for a local orchestra in St-Maurice, Switzerland. We support young musicians by hiring musical coaches to accompany our projects, and performing two concerts a year for our communities. I've been with them for seven years, and I feel so lucky to be able to perform the works of great composers of the past. If you would like to support the orchestra, please click a "I'm a fan" at our crowdfunding page www.lokalhelden.ch/os-m and share our project on your socials (unfortunately, the webpage is not in English). Thanks again for coming around to appreciate beauty together,
EDIT - The crowdfunding goal has been met, thank you so much!
Orfeas
I always enjoy Debussy 😂
ah yes Debussy
had to do a double take reading this
뿅
I'm going to be the curmudgeon being off-put by the Debussy (especially the volume of it)! I'd always rather prefer Ravel, it's more attractor, err, attractive. Or why not some cello music then? (It doesn't even have to be Bach's unaccompanied cello suites, some Geminiani, or the Trio in Eb by Schubert). Yes, of course, I turned off the sound. I know how to Internet, but it would have been nice! :)
Brilliant video. Thank you for this and using your appreciation for music to make an adroit partner of performance of dynamics and sound.
Bro makes a single video and it is incredible
Never in my life have I felt the need to have a screensaver. Until now.
The music and the colours turn these math equation into videos of awe and the very definition of beauty itself.
If you ever feel like your computer has been getting too complacent, this video was an otherworldly experience that felt much longer than 6 minutes and I would love to see some of these go on for an hour or more, especially with more classical music!
I love how this reminds me of that one courage the cowardly dog episode with cosmos squids
and here I thought I had seen every episode
You can take any moment of that animation and turn it into a beautiful wallpaper
6:20
i'm blaming you for making me get addicted to watching these, these are just satisfying to watch.
Just got this recommended and im glad it did. I have a feeling this will blow up
Such beautiful visualizations of mathematical graphs... Mesmerizing work, well done!
This is - on a surface level - some kind of art. You've done an amazing job!
Why on a surface level? :)
Absolutely Beautiful, thank you for taking the time to create this. 🙏👏👏
I'd love to see these in VR, the added depth perception would make it look even nicer I bet.
why do we possess the ability to find beauty in a concept so abstracted from the nature we evolved in and from? why did we evolve the ability to receive pleasure upon observing certain mathematical functions?
The Aizawa and Halvorsen Attractors are just so breathtaking.
Halvorsen Attractor remind me Treyarch emblem or Penrose triangle
Maths and Music; order out of chaos. What a divinely inspired video. 👏👏👏👏👏👏
So beautiful! This was so satisfying to watch! Great video 👏🏿😍
This is certainly an inspiration ..that tomorrow I'll be writing my exam on dynamical systems.!
I've struggled with maths for a while now, and avoided it to boot, but lately, I'm discovering more and more of an interest in it, despite being less than novice. The visuals and the equations that bring them to life are fascinating, and I was wondering where I should start, if I wanted to learn the mechanisms behind attractors.
Thank you for making this video, it has ignited in me a curiosity for math I didn't know existed!
The UA-cam channel "3Blue1Brown" makes great math videos, some are for novices like you and I, and some are more advanced.
I know this was posted over a year ago, but the branch of maths related to this phenomenon is called "chaos theory". It's part of a larger branch called "differential equations". In brief, differential equations deal with how systems respond to change. For example, if you set a block on a spring into motion, how would it move over time? Or, like in the Lorenz Attractor case, if you put an air particle near a flame, how does it move over time? At the start of the video, the three equations that were shown were three differential equations. dx/dt represents the rate of change in x position over time (i.e. x-velocity) and then there are equivalent equations for the y and z dimensions. How these equations govern the position of the air particles over time drastically change based on the initial conditions of the air particle, leading to the beautiful patterns seen.
This is absolutely beautiful, thank you so much for posting!
Thank you for making this :)
The animation, the music, the voice, the smoothness. Please make more videos
Very fascinating. Looks like energy being simulated.
Someone please turn this into a 3D display that can sit on my desk.
Curious to hear what it would sound like if each point was assigned a midi number/event on a synthesizer
How would you assign it for 3d coordonates?
@@killianobrien2007or infinite points
The symmetry in Halvorsen's attractor is majestically beautiful ! Well done !
This is stunning. The excellent music choice makes it remind me of a Len Lye film. I could watch hours of this set to every debussey piece.
wow that was amasing!!
thanks for sharing your work :) My kids really loved it :)))
my gosh these are each gorgeous showcases, i think my favourite is the nose hoover attractor
I turned on cryochamber's live stream and this at the same time and muted this ( but with captions ) and it matched waaaaay better than I was expecting lol great.
i love that these are utterly deterministic, and reversible, just like fluids shear mixing in a thin film between two concentric cylinders (a Couette cell)
Chaos and Love.
You have found an amazing discovery my friend.
I am a very creative person, and this video strikes at the cores of my abilities. So thank you, just for sharing this. Beautiful find.
Absolutely beautiful! You’re really talented!
The Debussy works so well with the equations. Like a grand fireworks display. Thank you! 😊
If possible, I'd like to see a higher "Resolution" on the lines, there are some minor jagged egdes when the particles go very fast, such as at 3:28 on the left side. Also, it would be nice for some of them to get a more zoomed out view. Other than that very nicely done! Also I love your voice, it feels like it really fits with the visuals and music.
Thanks man, I appreciate it very very much. I saved this video for later to take notes and research all of those!
If it’s not been done already, these would make an awesome drone display.
my life has been forever changed by a video that i clicked on because i thought it looked cool.
This was beautiful. Thank you.
Perfect choice of music!
The problem with chaos might be in using of concept of dimensions. Universe is not deterministic and can’t be divided into directions like math tries to determine it
Adding dx, dy, dz to x,y,z repeatedly is called vertex integration. It is an easy way to break down and simulate a lot of complex interactions. Often used in games. (I was a game developer) in the early days every game was it's own engine. These days the 'game engine' takes care of all this 'complex' mathmatics. But if you have the brainpower for it, it is amazing to play around with. You'll never look at the world the same. I made (and sold) about 200 of these early games-that-are-game-engines in my life. Very thankful for that experience. Attractors are important, but they are just the tip of the iceberg.. most things are not really expressable in language.. possibly in maths.. currently trying that..
Brilliant and evocative, thank you. We are exploring how these might represent the dynamics of ecological systems.
Fantastic video! Debussy was a very good choice for music.
Perfectly selected music, thank you for tbis
The second one gave me fireworks wibe from childhood. I hope there is a longer version.
We need more of these, please. And we need them a couple hours long. Thanks lmao
I love mathematical art like this, but I feel like you could have done more to make the structures of these more understandable. I feel like picking a bunch of points really close together to start makes it hard to follow some of them, though it looks awesome on the Aizawa one, some of them don’t seem to be entirely on screen, like the 3-cells CNN, Newton-Leipnik and Bouali, and there should be some way to show more of the 3D structure of them (for example, points closer to the camera are larger).
Ie, maybe you could start by showing the divergence from a cluster of points like you do here, but then fill the attractor out with some more evenly divided points and start moving the camera around like how you initially showed Lorentz.
Also, some of the names for these are hilarious, especially Nose-Hoover xD.
There's just something weirdly calming about this looking organic.
that was unbelievable, beautiful video
I want to watch this in vr. Seeing this in a three dimensional plane with some soft music would be beautiful and likely hypnotic.
These are incredibly beautiful thank you
it looks like stars dancing on the canvas of a blank cosmos.
so beautiful whit the music. excelent selection. thanks
Chaotic attractor? Uh, yeah, my boyfriend.
Videos like these make great backgrounds
This is such a quality video! Thanks so much
This is very cool! I wonder what it would sound like if you added sounds whose pitch, volume, and frequency corresponded to the position, speed and velocity of the points
Need a masterclass on how to recreate this. It's wonderful.
for something chaotic, the shapes they make are suspiciously ordered representations of certain 3d shapes
Good choice of music - _Engulfed Cathedral_ - Debussy
I'm not a big fan of math but I appreciate the beautiful things that its created, such as these "attractors" as you call them. Great video mate.
"Mommy, what constellation is that?"
"Shut up, have a cookie."
Something about this reminds me of my DMT trips.
The way that everything 'swings'.
Unfolding endlessly.
A Brilliant choice of an auditory attractor..🎼
These simulations are nice to look at, though I admit I had some trouble determining if a point was moving towards or away from a camera, what with the viewport being at a fixed position.
Perhaps if the dots got bigger as they got closer, and shrank when they moved away?
Oh well, it's a minor nitpick at most. Good video.
Yeah, would definitely help make the 3D structure more understandable.
Or make it into a tiny program with video game style controls. It would probably fit in less than 50kb
The sparkly colored dots whenever the darkness in my vision shows up be like:
Thank you in the deepest sense. : )
I am convinced this is how galaxies are formed and that math is the answer to the universe.
Math is the answer to the universe but galaxies are formed with wayy more variables and equations and complexity. I recently read that 3D slime mold simulations are the best we have for how galaxies first formed after the Big Bang, but only manage to simulate a single aspect behind it all.
One card in a Blackjack deck. A deck of many decks.
Beautiful, truly.
I woulve liked the same explanation at the beginning for each light show afterwards, but still a very nice video.
This is beautiful and I'd love to do something like this in VR
I thank you, earnestly, for sharing, my favorite is the one at 1:48
That's so beautiful thanks for sharing
I don't understand math behind these but chaos is truly amazing and beautiful
Perfect for a wallpaper!
The Tinkerbell map is a fun one! Just had a 4 week crash course in chaotic dynamics. Was fascinating to see how laminar fluid flow transitions into turbulence. Got an A* on my report too ;)
I could watch these for hours
chaos is a beautiful thing, unpredictable and incalculable by the numbers that were meant to know everything. a true definition of free will
This is what I see when I listen to exceptional music (Vivaldi, Debussy, etc). It’s so breathtaking that it sometimes make my legs wobble.
This is great, will done!
All chaotic systems have at least 1 strange attractor in their phase space -> there are at least as many attractors as there are chaotic systems (that's where they get the fractal quality). It's been a while but I want to say any partition of the subspace of a dynamical system which is an attractor would also be an attractor as well. If that is the case, it's really a combinatorial problem; how many unique partitions of the basin of the subspace exist? How big is the set of time functions F={f(a,t)| a in A -> f(a,t) = b, b in B(A), for all t greater than n}? It's probably a lot, but my hands are waving more than the queen on coronation day.
Math is the beautiful instrument by which the song of existence is played.
I just sparked up a spliff as I started watching your video. There’s no other way to say this so the following is via the microphone….
Wow like this is just phenomenal the Newton tractor is wow like I am really impressed this is phenomenal I don’t think in words do this justice I put this up on my 68 inch screen and turn off the lights And it’s just magical the hell boss in the tractor how boards in a tractor ha ha ha ha and that you can’t work out what I’m saying but mate unreel Coralie Coralie enjoy this thoroughly enjoyed all of it. Thank you
They look like they're dancing, it's so beautiful
Thanks UA-cam algo for recommending this video after 3years
Keep up the good work 👏 😊
Great video!
I'm currently experimenting with non curved space attractors. They look similar to CPU architecture.
make a video
@@DiamondSane yes please
I think this i what death would feel like. A forever show of chaotic attractors. Such a delight.