Are there other Chaotic Attractors?
ฝัง
- เผยแพร่เมื่อ 19 มี.ค. 2019
- A showcase of chaotic dynamical systems, similar to the Lorenz Attractor, coded in C++ and SFML.
Github: github.com/xMissingno/Coding-...
Mathstodon: mathstodon.xyz/@xMissingno
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Equations: www.3d-meier.de/tut19/Seite0.html
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
@@somaharanyi7943 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!
@@somaharanyi7943 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
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.
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
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?
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?
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...
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.
Anyone who uses Debussy to set the mood for complex beautiful animations gets my upvote automatically.
Debussy??? 🤨🤨🤨😳😳
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
Ah, math fireworks. Every day can be the 4th of July when you love math.
love this comment!
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.
the music fits beautifully with the movements... simply beautiful!
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
Maths and Music; order out of chaos. What a divinely inspired video. 👏👏👏👏👏👏
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!
You can take any moment of that animation and turn it into a beautiful wallpaper
6:20
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
Such beautiful visualizations of mathematical graphs... Mesmerizing work, well done!
This is absolutely beautiful, thank you so much for posting!
The music and the colours turn these math equation into videos of awe and the very definition of beauty itself.
I'd love to see these in VR, the added depth perception would make it look even nicer I bet.
Thank you for making this :)
wow that was amasing!!
thanks for sharing your work :) My kids really loved it :)))
Absolutely beautiful! You’re really talented!
Absolutely Beautiful, thank you for taking the time to create this. 🙏👏👏
The Aizawa and Halvorsen Attractors are just so breathtaking.
Halvorsen Attractor remind me Treyarch emblem or Penrose triangle
Just got this recommended and im glad it did. I have a feeling this will blow up
The symmetry in Halvorsen's attractor is majestically beautiful ! Well done !
This was beautiful. Thank you.
This is - on a surface level - some kind of art. You've done an amazing job!
Why on a surface level? :)
This is certainly an inspiration ..that tomorrow I'll be writing my exam on dynamical systems.!
The animation, the music, the voice, the smoothness. Please make more videos
so beautiful whit the music. excelent selection. thanks
These are incredibly beautiful thank you
Thanks man, I appreciate it very very much. I saved this video for later to take notes and research all of those!
Perfectly selected music, thank you for tbis
This was beautiful. Thanks for sharing 👌👌
Perfect choice of music!
This is such a quality video! Thanks so much
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.
Absolutely mesmerizing.
That's so beautiful thanks for sharing
Bro makes a single video and it is incredible
my gosh these are each gorgeous showcases, i think my favourite is the nose hoover attractor
Beautiful and simple, love it :)
Beautiful work!
Videos like these make great backgrounds
so beautiful, thanks!
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.
This is great, will done!
Beautiful, truly.
Fantastic video! Debussy was a very good choice for music.
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.
that was unbelievable, beautiful video
beautiful work, thank you
We need more of these, please. And we need them a couple hours long. Thanks lmao
Brilliant and evocative, thank you. We are exploring how these might represent the dynamics of ecological systems.
Holy hell this is amazing.
Great job!
i'm blaming you for making me get addicted to watching these, these are just satisfying to watch.
Never in my life have I felt the need to have a screensaver. Until now.
Thank you in the deepest sense. : )
Just beautiful
Very fascinating. Looks like energy being simulated.
The Debussy works so well with the equations. Like a grand fireworks display. Thank you! 😊
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.
Pure perfection👏👏👏👏
This is beautiful, thank you
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 the 3D nature 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.
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
This is beautiful and I'd love to do something like this in VR
Perfect for a wallpaper!
A work of art
Beautiful shader!
Thank you for the video
I could watch these for hours
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.
This is incredible
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 TH-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.
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)
breathtakingly beautiful
Magnificient!
A Brilliant choice of an auditory attractor..🎼
thank you for this video
epic video thank you for making this
Absolutely stunning--time to read up on chaos theory.
Theres chaos in your dp
it looks like stars dancing on the canvas of a blank cosmos.
Amazing!!!!
This made my day
This is a very good video.
Beautiful
Need a masterclass on how to recreate this. It's wonderful.
Good choice of music - _Engulfed Cathedral_ - Debussy
The second one gave me fireworks wibe from childhood. I hope there is a longer version.
This is sick
so thats how screensaver were made
Just another video to watch at 3 am
underrated video.
I woulve liked the same explanation at the beginning for each light show afterwards, but still a very nice video.
Wonderful!