The Chaotic Beauty of the Double Pendulum Fractal

[@ellingeidbo8469]

Breaking computers by asking questions too hard for them is one of my favorite things to do.

[@nicogsplayground]

the divide by 0 is still the one and original

[@dynhoyw]

@@nicogsplayground "little Timmy, what did i tell you about dividing by zero? now you've created a singularity and caused havoc in the solar system."

[@slightfimulator4888]

Accidentally checking node_modules into git is the new hotness.

[@carstenmohler629]

How on earth does this only have 1.000 views? Everything from the editing, to his voice, to the way things are demonstrated and explained is so well done

[@nicogsplayground]

Thank you so much 🙏🏻 Appreciate it!

[@nicogsplayground]

full disclosure: As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅

[@FengXingFengXing]

¡Great animacion! Video need more detail. • ¿Pèndulums in grid all have equal length? • Range x and y axis is -π; π • ¿What is start velocity? • ¿How select color? • Range x and y for last grid is 0; 2π Should compare equal level geography: • Butterfly in Brasil; tornado in US or • Butterfly in Amazonas; tornado in Texas

[@Flesh_Wizard]

Probably posted from Mars 😂

[@XenoghostTV]

The voice is AI dude lol

[@RecordedSpace0880]

Visualizing the varying angles progression as a fractal evolving over time is such a creative way to view chaos theory that I haven't seen anywhere else before. And it looks so beautiful.

[@nicogsplayground]

Thank you so much 🙏🏻

[@Savahax]

Woah amazing. That's the typical misunderstanding, or rather misuse of fractals shown right here. A fractal typically isn't self familiar. The reason we focus on those is because they're beautiful and easily produced but a fractal usually is way more chaotic, like the one shown here. It's awesome man, great vid

[@samevans4834]

Some clips from this video could be dropped right into an Apple keynote and no one would bat an eye.

[@nicogsplayground]

That’s a huge compliment! Thank you so much 🙏🏻

[@nicogsplayground]

(if anyone at Apple would be reading this: email me oxxo)

[@Makememesandmore]

Who agrees this guy is criminally underrated:

[@ztunedd]

like beggar

[@Froany]

Thank you for sharing such beautiful, inspiring animations!!

[@DanteValenzuela-fg4co]

Finally my home of content in the internet

[@thelightmare]

Superb video, very nicely explained ! I would have loved to see a zoom into the fractal !

[@nicogsplayground]

Thank you so much 🙏🏻 might create some extra visual content next week, i’ll keep you posted 🙆‍♂️

[@dan2te2]

To find videos like these, that are high quality and full of information is a rarity these days. So thanks Nicogs Playground, Great Video!

[@WhyIsJupiterInTheFridge]

For anyone wondering: Blue = Pendulum at lowest Red = Pendulum at highest Darker = Low Velocity Brighter = High Velocity

[@AlanZucconi]

The production on this video is SO! high! 💪

[@nicogsplayground]

Appreciate it! Something specific that you liked? 🙏

[@msergejev]

@@nicogsplayground Specifically, all of it :D

[@FoxDog1080]

2:07 I love how the corners can become a seizure trigger I don't know how else to describe it, this is not a negative comment

[@EdwardNavu]

It's like splitting hairs when the differences accumulate to the point the conditions part ways and become no longer similar

[@Byron_Vega]

I love the narration style, it brings back so many memories.

[@Makememesandmore]

Bro's David Attenborough

[@pnintetr]

Beautiful representation :) I have always wondered whether the double pendulum would retain any sort of continuity after having heard of chaos theory. But hey, it did (somehow)! and that is a nice looking turbulence.

[@nicogsplayground]

Thank you so much 🙏🏻 appreciate it!

[@朕是神]

2:05 there's obviously something wrong with this simulation. Look at the pendulums at the bottom right corner. It's spinning around faster and faster, which means the mechanical energy involved is increasing over time. Now, if I were to guess it's rounding errors which is unavoidable, but there are some simple error smoothing you can add: for every frame, after you calculate the angular velocity/angles of the next frame, first calculate the total energy invovled with that, and then normalize it back to the value you started with, then have the normalized result be fed into the next frame. You'll still get slightly off results, but it won't be quite this drastic.

[@anotherbrickinthewall001]

I think you made a mistake in concluding that mechanical energy involved is increasing over time, because here we have two pendulums which are exchanging energy with each other while keeping the total energy constant. What we see as spinning faster is one of the pendulums while the other pendulum swings slowly to conserve energy.

[@fishercawkey]

It depends on the numerical integration scheme being used. Because the simulated double pendulum model has no damping, certain numerical integration schemes will indeed cause what looks like an increase in mechanical energy over time. I was just earlier today watching a great video by Steve Brunton called "Stability of Forward Euler and Backward Euler Integration Schemes for Differential Equations" that explores this for a basic numerical integration scheme and a linear ODE.

[@Makememesandmore]

Guys, the new David Attenborough just dropped!

[@sdf_96]

love this video, cool asf. surprised you don't have way more views

[@calculator_gaming]

I can't tell if this is an AI generated voice or a real voice becuase it never changes in tone (thats a compliment)

[@nicogsplayground]

@@calculator_gaming As I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅

[@f7029]

Very well made video!!! Super interesting. I'd love to see a tutorial of how to visualize things like this on computer.

[@nicogsplayground]

Thank you so much 🙏🏻 something in particular that stood for you? I created this mostly by coding it myself in Javascript utilising the p5js library. I would recommend checking out “The Coding Train” for full tutorials on how to make these kind of visuals :🙏✨✨🙆‍♂️

[@f7029]

@@nicogsplayground I find the probability heat map overtime especially inspiring. Its almost like blending together spatial-temporal dimensions into a new realm of its own.

[@yevhenlos6255]

Time to update my milkdrop plugin. Superb visuals here.

[@nicogsplayground]

At least 20y since I’ve heard of Milkdrop waw haha! & Thank you so much 🙏🏻 anything in particular that you liked? 🙆‍♂️

[@kiksu1]

Wow, this is cool. Looks very much like photoelasticity.

[@nicogsplayground]

Thank you so much 🙏🏻 I did not know the term photoelasticity, had to google it, but you are 100% right, looks a lot like these holographic reflections!

[@nutzeeer]

Its beautifully smooth

[@FoxDog1080]

Add a third dimension for the percentage of the length the joint is at and take different planar sections of it to see what's happening

[@ConnoisseurOfExistence]

What is chaos? All I've ever seen are different states of order.

[@nicogsplayground]

Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal.

[@ConnoisseurOfExistence]

@@nicogsplayground Thanks for your answer. Nothing is random, therefore chaos doesn't exist. In fact, I can't even grasp what chaos would be, or how even hypothetically could exist...

[@nicogsplayground]

@@ConnoisseurOfExistence that’s why it’s called Chaos Theory. The idea isn’t that something behaves randomly, one can predict it’s behaviour given the initial conditions. But when we try to determine the initial conditions based on it’s behaviour, it get’s pretty hard because of the “chaos”.

[@ConnoisseurOfExistence]

@@nicogsplayground Maybe we can't even determine its exact behavior (future state, position and momentum) from the initial conditions, without actually letting it play out. They call it computational irreducibility. Many complex systems are like that. Beautiful video, by the way. I shared it in many places. I love fractals!

[@nicholasjacobson3712]

​@ConnoisseurOfExistence Plenty of things are random. Statistics and Thermodynamics rely on randomness existing to be accurate sciences.

[@holygod8440]

this is so good, it deserves a place in the yt trends ngl

[@nicogsplayground]

Thank you so much broo 🙏🏻

[@jeffreygordon7194]

Wonderful! Thanks for making this!

[@nicogsplayground]

Thanks Jeffrey! Appreciate it!

[@ClarkPotter]

Great video. Sub'd. I intellectually love this sort of thing most deeply of all. It's a category error to say "...how chaos theory shapes our world." Chaos Theory involves our attempt to model chaotic phenomena. It's not the phenomena itself, which is what shapes our world. That statement conflates the map with the territory.

[@nicogsplayground]

Thank you so much Clark 🙏🏻 But doesn’t our attempt to model the phenomenon shape our world too? Take The three body problem, this shapes our understanding of the world and therefore shapes our world no? 🙆‍♂️ (my apologies if I understood the Q wrong) But apart from the error anything in particular that you loved?🙆‍♂️✨

[@TobiasSchoenke]

Wow really great video - didn´t know these kinds of fractals - loving it! 👍

[@nicogsplayground]

Thank you so much Tobias 🙏🏻 Anything in particular that stood out for you?

[@amazingnacho2177]

Bro what the fuck. What a masterpiece

[@nicogsplayground]

Ayeeee appreciate it a lot! 😂🙆‍♂️🙏

[@Miaumiau3333]

Awesome video! I think you didn't explain an important detail though, what do the colors represent?

[@nicogsplayground]

Converted the angles, which we mapped on the grid to colors, rgb values. (01:57) But you are right that I should've probably put more emphasise on that!

[@Miaumiau3333]

​@@nicogsplayground Makes sense. Since this looks like a continuous map and angles need to jump back to 0 if they go past 2π, you would need to map the sine or dot product or something like that to RGB space. Do you know the exact details?

[@nicogsplayground]

@@Miaumiau3333have to double check but I think: R: 255/2 + 255/2 * Sin(angle 1) * cos(angle 2) G: 255/2 + 255/2 * Sin(angle 1) * sin(angle 2) B: 255/2 + 255/2 * cos(angle 1)

[@Miaumiau3333]

@@nicogsplayground This looks good, thanks Nicog!

[@bigmouthfisheyes]

Very trippy. Will add it to my list of things to watch if I ever try mushrooms.

[@luizhenriqueamaralcosta629]

Beauty

[@vaakdemandante8772]

A similar 2D fractal is created when you plot starting angle of the hands of the pendulum. I wonder how a 4D fractal would look like that combines the dimensions of hands lengths and their starting angles.

[@fishercawkey]

Great work! It reminds me of "Up and Down the Ladder of Abstraction" by Bret Victor -- put that into your search engine of choice if you haven't seen it yet. It may give you more inspiration!

[@beaverbuoy3011]

SO COOL

[@ShayerSUtsho]

Could the unchanging center bit give us information on which initial conditions give us the longest duration of predictable outcomes?

[@thecrackfunkledone]

I need like all of those visuals as a gif or something

[@bean751-n2y]

This has only 18k views. Outrageous.

[@nicogsplayground]

@@bean751-n2y I would even say: deplorable

[@progamer69243]

Underrated animation

[@nicogsplayground]

@@progamer69243 I appreciate the compliment Mario! Was there a scene or specific animation that you liked in particular? Thanks again 🙏🙏🙏

[@jojosumit7690]

Beautiful

[@sauerkrautlanguage]

what determines the color of the pendulum in this simulation?

[@nicogsplayground]

The only variables that evolve over time: the angles made by the legs of the pendulum, hence why I mapped it on a grid 😅🙆‍♂️

[@MEGAMeetsmeh]

Sneak peek at Pendulum’s next album cover

[@Stagnated541]

This video is better than all the ones I've seen so far.

[@nicogsplayground]

Thank you so much 🙏🏻 Anything specific that it made it better than all the other ones? Feedback is much appreciated!!!

[@Stagnated541]

​@@nicogsplaygroundIn my opinion your videos are perfect. If you want more views to begin sharing your content, I would try to get promoted by similar youtubers. I saw that some of popular youtubers actually promoted small creators.

[@Stagnated541]

​@@nicogsplaygroundoh, and a lot of tags

[@IceMan-i9o]

perfect video everyone watch this.

[@nicogsplayground]

Appreciate it IceMan! Anything specific that you liked?

[@Schöenebuddy]

Everybody gangsta until triple pendulum

[@nicogsplayground]

I was already sweating now tbh

[@LinkenCV]

😳 triple angles, 3D-version of the fractal. But how to calculate the color in this case. For 2 angles I assume sin(a,b) and 0=red, 1=violet. Is there stereoscopic variant 🤔

[@Evan----]

Awesome

[@nicogsplayground]

Thank you so much Evan 🙏🏻 Something in particular that you enjoyed? Can always use the feedback

[@Evan----]

@@nicogsplayground animations are quality

[@nicogsplayground]

@@Evan---- Thanks!!! They often take a lot of time. Keyframing and tweaking curves so the speed and motion fits the whole composition and story line, can take hours for maybe 0.8 seconds of motion. Knowing that it doesn't go unnoticed by others really makes my day, appreciate it!

[@adrienledoux357]

Waoh! Can you run the simulation longer?

[@nicogsplayground]

@@adrienledoux357 will upload some extra content, with some zoom in’s etc next week 🙆‍♂️ will keep you posted ✨

[@HarishBabuM]

@@nicogsplayground what's the softwares used?

[@nicogsplayground]

@@HarishBabuM Coded in Javascript using the p5js library 🙆‍♂️ Will share the github online version soon probably ✨anything in particular that stood out for you?

[@Rbtdkawaii]

what hidden gem did I just stumble into?

[@chasemarangu]

Your channel rocks. Subscribed. This is so useful of a visualization of the notorious double pendulum!

[@nicogsplayground]

Thank you so much Chase 🙏🏻 Glad you find it useful!!!! Makes my day

[@wertibl3]

Would this be considered a fractal? I thought fractals require self-similarity... Wouldn't this be a subset of samples of the phase space of the system evolving as you scroll forward through time? Sorry if this is a dumb question.

[@nicogsplayground]

No such thing as dumb questions, I had to google it to be sure, but Self similiarity includes Multifractal scaling

[@Oshic1273]

May i ask where thou got the music from

[@nicogsplayground]

I used several audio tracks from several libraries I bought over the years, some are from premium beat, others from ezco and others like that. Not a specific artist or full song

[@dan.w.2432]

I've seen this fractal on Sam Maksimovich's channel before, but less well explained. This is a beautiful way to depict how that fractal is formed, my only criticism is the video transcript feels verbose without adding much, like it's been generated with chatgpt. It also doesn't help that the voice is AI generated.

[@nicogsplayground]

Thank you so much 🙏🏻 I don’t see it as criticism, but as valuable feedback! I used AI to help with the writing of my intro and outro otherwise only spelling was corrected as English is my third language. Thanks for pointing that out! As I hate recording my voice I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over and the pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅 Anything in particular that stood out for you on how I explained it? Thanks in advance for the feedback! 🙏🙆‍♂️

[@Milan_Rosko]

This is not a fractal. Fractals exhibit self-similarity across scales and typically have a fractal dimension, representing infinite detail at any level of magnification. While fractals exhibit deterministic patterns even within their complexity, the compound double pendulum's chaotic nature lacks a recursive or self-similar structure that would persist infinitely as with fractals. Also we are faced with undecidability. In theory I could arrange a configuration that "stops" at a certain depth without for you to know in advance by trivial means.

[@Nicogs]

Fractals don’t have to be self similar

[@amazingnacho2177]

Bro just updated chaos theory.

[@wonkyfug]

I got my lasagna dude! 😎

[@Pingu_astrocat21]

This is so coooool

[@LivingBreathingRedFlag]

Ten out of ten.

[@nicogsplayground]

@@LivingBreathingRedFlag 🫡 Thank you so much, was there anything specific that stood out for you (or any feedback)?

[@yassinemehdi7688]

Why does this channel only have 422 subscribers?

[@nicogsplayground]

Asking myself that question every single day 🥹✨🙆‍♂️

[@nachoalk]

How did you animated this? o:

[@nicogsplayground]

All of the simulations where created using Javascript & the p5js library. Then I put everything together in Premiere Pro & animated the B-roll + some of the explanations. For example the grid was simulated in JS but I animated the x-axis & y-axis transition in After Effects :))

[@nachoalk]

@@nicogsplayground you are f#cking talented bro

[@nicogsplayground]

@@nachoalk ayeee appreciate it!!!!

[@adrienledoux357]

Can you do it with n-pendulum?

[@nicogsplayground]

@@adrienledoux357 In theory yes, but then we should have an n-axis grid, which wouldn’t create anything interesting I guess haha

[@ClarkPotter]

Even 3D glasses wouldn't be enough for that. You'd need nD glasses, not to mention a biology that could make sense of it.

[@thedisappointment7323]

It’s 3am and I’m somewhere here

[@nicogsplayground]

3am vibez guaranteed

[@kennylex]

Almost looks like the outside of a Julia set at

[@nicogsplayground]

I did not notice that, but now that you say so…. Orrrrrrr the Julia set looks like the inside of the Double Pendulum Fractal

[@g-pc6wp]

i wonder if this would make a good wallpaper

[@TheDiegofernando13]

So, there is a pattern?

[@somerandomguyontheinternet1553]

holy shit this is sick

[@ukhaanzaya-z8d]

how do you even convert angels into points? 😕😕😕😕😕😕😕😕😕😕😕😕

[@nicogsplayground]

(x,y) = (theta1, theta2) = (first angle, second angle)

[@mansamishra9323]

Blud thinks he is an artist (is one f*cking genius ) ❤

[@-_Nuke_-]

They are saying that "Chaos theory suggests that minuscule changes in initial conditions can lead to massive differences later on" But that is WRONG. The particular part that is wrong is the "minuscule changes". The changes are not "minuscule", they are *INFINITESIMAL* and that is where chaos arises. We have a function, a real - DETERMINISTIC - function, that perfectly describes from the initial conditions that we gave to the computer of the experiment... But in order for that function to be calculated we need INFINITE amount of time... Because the function's graph is a fractal... And thus, *INFINITESIMAL* changes can create non-infinitesimal differences later on. Thus, we can never fully create a perfect model for our experiment, because the information that we need to know is infinite.

[@nicogsplayground]

@@-_Nuke_- Small differences in initial conditions, such as those due to errors in measurements or due to rounding errors in numerical computation, can yield widely diverging outcomes for such dynamical systems, rendering long-term prediction of their behavior impossible in general. This can happen even though these systems are deterministic, meaning that their future behavior follows a unique evolution and is fully determined by their initial conditions, with no random elements involved. In other words, the deterministic nature of these systems does not make them predictable. This behavior is known as deterministic chaos, or simply chaos. Sources: Kellert, Stephen H. (1993). In the Wake of Chaos: Unpredictable Order in Dynamical Systems. University of Chicago Press. p. 32. ISBN 978-0-226-42976-2. Bishop, Robert (2017), "Chaos", in Zalta, Edward N. (ed.), The Stanford Encyclopedia of Philosophy (Spring 2017 ed.), Metaphysics Research Lab, Stanford University Werndl, Charlotte (2009). "What are the New Implications of Chaos for Unpredictability?". The British Journal for the Philosophy of Science. 60 (1): 195-220. arXiv:1310.1576. doi:10.1093/bjps/axn053. S2CID 354849.

[@-_Nuke_-]

@@nicogsplayground I agree! My nitpicking part is that these differences in initial conditions don't need to be small, because the word "small" is still a huge word in the world of chaos. Even an infinitesimally small difference will be enough for the whole thing to derail into chaos. I just made this comment to really emphasize the sheer infinity in the nature of chaos.

[@Carlo-zs5lw]

Absurd, what have you used to create this?

[@nicogsplayground]

Thank you so much 🙏🏻 Using Javascript & the p5js library for all the simulations 🙆‍♂️🙆‍♂️

[@AstroEli133]

bros narrating a nature documentary 💀💀💀

[@xoxoheartz]

bro that graphics card probably got cooked 😭😭😭

[@nicogsplayground]

@@xoxoheartz 😂 the power of GPU va CPU 💪

[@Handleussy]

it looks like starglow from after effects

[@nicogsplayground]

The plugin? Never used it tbh, what part of it’s functionality has a similar look? 👀 Could be interesting for future video’s 🙆‍♂️🙆‍♂️

[@Handleussy]

@@nicogsplayground the warping and the colors!

[@romansapp5219]

I’d love to see this fractal projected onto a torus

[@pyropulseIXXI]

Is this actually a fractal? From my naive understanding, it doesn't seem to be a fractal

[@skylark.kraken]

its*

[@TheCaregiverSITMOB]

lol i thought you were a tts

[@ray-pu8vt]

As much as i love the visuals, sound, and explanation (it was very well made), please credit Sam Maksimovich for his first original take on this concept (kzbin.info/www/bejne/pGitfGd-qZ2ebq8). It is so clearly tied to his video on it, even using the same concept and even color mapping.

[@nicogsplayground]

@@ray-pu8vt To be completely honest, I came by a paper with the same name written by Jeremy S. Heyl more than 16 years ago. The next and basically only source I worked with was a blog post by Jason on the softologyblog While working on the visualisation someone on reddit replied with a code snippet, with a very neat implementation for the colors coming from Nikolai Mikuszeit, published in 2015, which on its turn was based on the colors from a book: Symmetry in Chaos: A search for Pattern in Mathematics, Art, and Nature, by Micheal Field and Martin Golubitsky. As I used different measurements I tweaked it so the colors would match. It is only after coding the project, putting it together in a video & finishing it all together that I discovered the KZbin video by Sam which is awesome! Although I do not mind giving credit where credit is due, but I don’t see how this should be the case here. I explained a mathematical phenomena, from a different perspective, and from a different input angle with Chaos Theory. Nor was Sam the first discovering the concept, nor the usage of the colors. But regardless, being the first to discover of a mathematical concept, is different from being the first to create something, in which credit would certainly be appropriate. In this case I don’t see how it would be appropriate nor fair to credit Sam. (And this is nothing against Sam or anyone else, love his video, and I will add this to the description + all the resources I did use to come to my visualisation, not because I think credit is due, but rather so that others can see another way of explaining the concept)

[@ray-pu8vt]

@@nicogsplayground Im terribly sorry for taking such a one sided perspective on your video. I now realize that i was wrong and that you had no real intention to directly copy Sam's video. Thanks for clarifying!

[@nicogsplayground]

@@ray-pu8vt That is 100% okey! In a world of social media we can let the one sided POV’s get the best of us, although we are aware another side of a story could exist. I respect your time & energy you put in defending someone’s work btw + The fact that you are aware of the other side now & decided to apologise is a something so rare in a comment section of a KZbin video, that I’m honestly so grateful for the reasonable & very mature comment. I appreciate you

[@c7hu1hu]

God(s) resides in chaos

[@tescOne]

"length and mass are constant variables" doesn't make much sense but the video was good

[@nicogsplayground]

Appreciate it! When simulating a double pendulum the mass of the two balls and the length of the legs connecting them stay constant and won’t change over time, that’s what I meant with “constant variables”. Meanwhile the position of the balls or the angles made by the legs are variables that change. I Should’ve said that indeed, thanks for the feedback!! 🙏🙏

[@MrVovsn]

I see symmetrical pattern, not chaos

[@nicogsplayground]

Motions in chaotic behavor is based on nonlinearity of the mechnical systems. However, chaos is not a random motion. As you have seen, the motion can be described with a specific nested structure, which is called fractal. around 02:52, the edges, every pixel represents a pendulum that had less than 0.001 deg in difference, but the vast amount of different colors shows the chaos that emerges from smaal initial differences. Many other chaotic systems look symmetrical btw 🙆‍♂

[@Philip-qq7ql]

Nice video but chatgpt ahh script

[@zombieregime]

Chaotic pattern does not equal fractal. And I really wish young people would stop misappropriating words like that. Of course, considering the way they do it so recklessly in so many other areas of their lives, I wont be holding my breath. It funny how entire generations celebrate science and understanding and acceptance, to just throw it all out the window and fight so voraciously for their misguided ideals. No, instead Ill be quietly weeping to myself, "they try to sound smart but they're just so arrogantly stupid..."

[@nicogsplayground]

I was tempted to simply write “Oke boomer” Someone who would write off a whole generation because of their incorrect & preconceived notions on this subject, could indeed be described as trying to sound smart but just being arrogantly stupid. Numerical simulations of the double pendulum reveal that the set of initial conditions within a set period of time has a fractal structure. Specfically, the boundary of this set is a fat fractal similar to that found by Farmer for a simple Hamiltonian logistic map, indicating that fat fractal boundaries may be a hallmark of chaos in non-linear Hamiltonian systems. Sources/further reading: J. D. Farmer, Physical Review Letters 55, 351 (1985). Or a great introduction to what I used as inspiration for this video, the “Double Pendulum Fractal” paper by Jeremy S. Heyl (Department of Physics and Astronomy, University of British Columbia, 2008)

[@Irondragon1945]

I wonder how much AI you used in the video making process. The wording of some sentences sounds kind of... non human.

[@nicogsplayground]

English is not my first, nor my second language. With dutch & frensh being my motherlanguages, some of the sentence structures might sound strange, except from some suggestions by NotionAI for better words & grammar, the script is written by le me. 🙆‍♂️ first time someone called my writing non-human, but I’ll take the compliment as “out of this world” 😅❤️

[@nicogsplayground]

Unless you where talking about the voice over, that’s actually a mistake 💀 As I hate recording my voice (accent, english yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅

[@Im_Rainrot]

Don't like the AI voice, feels soulless and uninteresting to listen for more than a few seconds.

[@nicogsplayground]

I agree! As mentioned before: I hate recording my voice (english second language yk) I always edit my video’s with an AI generated voice, so that by the time everything is edited I know every word of the voice over & at what pace I should say them. I only have to replace it with my voice recording, at the very last. Unfortunately I uploaded the wrong version & only realised the mistake a few hours after publishing 😅😅