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The logistic map connects fluid convection, neuron firing, the Mandelbrot set and so much more. Fasthosts Techie Test competition is now closed! Learn more about Fasthosts here: www.fasthosts.co.uk/veritasium Code for interactives is available below...

Animations, coding, interactives in this video by Jonny Hyman 🙌

Try the code yourself: github.com/jonnyhyman/Chaos

References:

James Gleick, Chaos

Steven Strogatz, Nonlinear Dynamics and Chaos

May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976). doi.org/10.1038/261459a0

Robert Shaw, The Dripping Faucet as a Model Chaotic System

archive.org/details/ShawRobertDrippingFaucetAsAModelChaoticSystem1984_201811/mode/2up

Crevier DW, Meister M. Synchronous period-doubling in flicker vision of salamander and man.

J Neurophysiol. 1998 Apr;79(4):1869-78.

Bing Jia, Huaguang Gu, Li Li, Xiaoyan Zhao. Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns Cogn Neurodyn (2012) 6:89-106 DOI 10.1007/s11571-011-9184-7

A Garfinkel, ML Spano, WL Ditto, JN Weiss. Controlling cardiac chaos

Science 28 Aug 1992: Vol. 257, Issue 5074, pp. 1230-1235 DOI: 10.1126/science.1519060

R. M. May, D. M. G. Wishart, J. Bray and R. L. Smith Chaos and the Dynamics of Biological Populations

Source: Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Vol. 413, No. 1844, Dynamical Chaos (Sep. 8, 1987), pp. 27-44

Chialvo, D., Gilmour Jr, R. & Jalife, J. Low dimensional chaos in cardiac tissue. Nature 343, 653-657 (1990). doi.org/10.1038/343653a0

Xujun Ye, Kenshi Sakai. A new modified resource budget model for nonlinear dynamics in citrus production. Chaos, Solitons and Fractals 87 (2016) 51-60

Libchaber, A. & Laroche, C. & Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. dx.doi.org/10.1051/jphyslet:01982004307021100. 43. 10.1051/jphyslet:01982004307021100.

Special thanks to Patreon Supporters:

Alfred Wallace, Arjun Chakroborty, Bryan Baker, DALE HORNE, Donal Botkin, halyoav, James Knight, Jasper Xin, Joar Wandborg, Lee Redden, Lyvann Ferrusca, Michael Krugman, Pindex, Ron Neal, Sam Lutfi, Tige Thorman, Vincent

Special thanks to:

Henry Reich for feedback on earlier versions of this video

Raquel Nuno for enduring many earlier iterations (including parts she filmed that were replaced)

Dianna Cowern for title suggestions and saying earlier versions weren't good

Heather Zinn Brooks for feedback on an earlier version.

Music from:

epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4"

ve42.co/Artlist "Busy World" "Children of Mystery"

Is there any relationship between the golden ratio, Pi and 4.669 ?

what happens when you try to reverse engineer a behaviour with a different ratio of bifurcation distances? i.e. imagine a fittingly compressed bifurcation curve and then think about what the initial function has to be.

wow it really changed my mind

bi-fur-cation, I get it!

2020 is chaotic enough, but this man is smart.

Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on

0:30 explain this to my bunnies

ఆ ఆi love u girl.

*I need so much study 🙄 *

It's turtles all the way down, the same way a brain cell looks exactly like the dark matter connections and pathways in our universe.

I still see the world with my eyes.. this video is so fake smh

mhm "active rabbits"

"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)

Mandelbrot on z axis looks like the universe a bit. I didn't understand HS algebra, but stuff I can see like this is totally different. Wow, this is amazing.

Everyone here were gangsta till he turned the Mandelbrot-set 3D

if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.

The cracks on my phone look like this 😭

When you say that rx grows exponentially, that in itself is a definite proof that you now nothing about math 👎

3:27 AM Me: hunched over the sink My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!

When I watched this video I though: I've seen lots of maths stuff... didnt change anything. EVERY TIME i turned on the sink, ever since and it started dripping I switch between chaotic and periodic. It really did change my life.... well a little bit.

That dripping faucet reminded me of my prostate.....

I dont think im fully understanding what Im seeing but I like it

Shout out to everyone who is here because they were impressed but also bamboozled by James Gleick’s “Chaos” :D

good

Great👍 Thank you so much🤓

30 January was my birthday!!😂

It's like discovering some of the software God used to write the Universe.

I love human beings!

Dude, you break my brain.

So this is how corona 1st wave 2nd wave 3rd wave 4th waves are predicted and govts around the world are forced to go on a merry-go-round lockdowns over and over around

I love this movie.

hey, can anyone help me simulate beautiful graphs like those with my own data? I mean most graph websites and software have ugly graphs

WAYTOODANK

if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.

2020 is chaotic enough, but this man is smart.

When someone loves you, the way they talk about you is different. You feel safe and comfortable.

based and epic

ok this was inspiring now Im gonna watch tiktok bella

Beautiful! Your best video 👏🏻👏🏻

Is this where the hype for "the curve" is coming from? Tbf there was also this series which iIrc was on Netflix with a whole society relying on statistical curves too much like the Spartans did with oracles.

Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on

You: Copy and paste Me: go on

The cracks on my phone look like this 😭

If you take a microscope and look at the even smaller cracks I'm sure it follows the same bifurcation

0:22 my love video :X.

What was illuminating for me is when you rotated the mandlebrot set with the population growth rate. Now it makes sense!

It is not possible to talk about the Mandelbrot set without using complex numbers.

4.669 is the tick rate of the RL server..?

(keanu voice): your content is incredibly fascinating! Beautiful approach 👏

So basically: everything in life follows a pattern, but that pattern is so subtle that most people will never notice unless they're specifically looking for it. At least, that's what I got out of it.

"Oh cool, the Mandelbrot-Set. I have seen that before." turns Mandelbrot-Set in 3D "What the ...?! That's illegal!"

Xrp ripple and bitcoin are making people rich af

The baptism of the holy spirit will do that first and more exactly, supernatural and science are coming together :) , the way it should be. Science started to have a an agenda with regards religion or God , the scientists started to become bias based instead of working from experimental proof.

Reality is made of non-linear patterns, and they repeat itself everywhere..."as above so below".fractals are the very pattern of energy that shapes matter. such great video and that axis rotation...speachless, gave me a whole new perspective on the mandelbrot set. thank you

has anyone read the paper posted by robert shaw that is listed in the video? just to confirm on page 15 there was a basic sketch of a mass stretching a string the releasing at the X0 of the system. for that equation what the x with two dots on top is the second prime of x correct and then the m with one dot is rounded or is that the prime of that number. I have done some internet research but cant find the answer, I will continue to try solving algebraically. the correct result in theory trend towards the chaotic entropy we learnt about in this video.

What calculation applications did you use on your mac?

nah... it didn't change anything with the way I see the world. sorry

The smarter i get, the dummer me is.all things being crazy.

Is my is my mother goose club out.

Has someone run an algorithm on the comments on this page? Because they are repeating under new names. I think someone is going to an EXTENSIVE effort to troll the point in the video.

Winner is left out of pocket. Sounds great.

x and x^2 are linearly independent. Yes, you can represent any function as a set of linearly independent functions. We can find a function for everything that can be said to be composed of linearly independent functions; let me save you some time and tell you that everything in this universe can be described as such. However, I am glad that people are at least thinking about this.

Very fascinating ! Thank you!

Enjoyed the video, but please stop saying everything is chaotic, or produces “chaos”! It is not chaotic, nor chaos. Everything you discussed demonstrated some kind of pattern. Even the periodic episodes of somewhat random-appearing behavior are part of a larger pattern. I also loved James Gleich, and physics, cosmology, ecology, etc. Some years ago, “chaos theory” led to the development of complex systems theory, which is fascinating, and more rigorous. Mathematics is everywhere, in the movements of traffic, crowds, flocks of birds and sheep, schools of fish; also in fluid flows, weather systems, climate change...It really is a small world after all. Best wishes for happy holidays. Please stay safe and healthy.

if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.

I love this movie.

What’s the point of this video ?

Soooooo ... Chaos is not Chaotic if you have ALL the beginning info !?

So my understanding is that rabbits must be eliminated before their reproduction breaks the game engine.

Figanbownd constant= controlled golden ratio maybe, not a mathematician by any means but really wanna wrap my head around more math

Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.

Thumbnail makes a cool album cover

If I had known how to do the simulations for rabbit population I would have preparing a manuscript on a peer reviewed journal😀. Great explanation.

my brain hurts now

This reminds me of “spooky action at a distance” Just rotating the Mandelbrot fractal in 3 dimensions was mind blowing... then the Feigenbaum constant...

Thats just amazing! thank you for putting it together!

/Говорит про спонсора видео/ Современные проблемы нуждаются в современном решение

"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)

The guy who programmed the universe used 4.669... as the seed for all random number generators, because he was lazy.

0:40 she is hot girl and sexygirl.

Complex than Dark web series

What if you teach a neural network to assume results with this ratio?

Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on

Sponsored by Fast Toasts

this is why I never change my point of view.

Took him exactly 58 seconds to throw me in the bushes with that theoretical maximum stuff. Maybe if I put my seat belt on. Nobody knew he was describing the coronavirus.

@pennie schirz Now, you gotta splain that, Lucy.

"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)

Teaching this to students only makes sense when you are not a STUDENT

If u were my physics teache that would of be my favorite class

So what you're saying is that the answer is 4.669? That is nowhere close to 42! I'm starting to think Adams made the whole thing up.

Like children having hmmm moments in an adult world, science has it's hmmm moments when looking at God's creation equations

I tend to think of things geometrically, so when you tell me that iterating a single hump function leads to a bifurcation series of individual humps, like that's the definition of iterating one hump. You have one hump. Then at the end of one hump, you do it again. Except per the quadratic equation and the natural existence of Phi, iterating one hump gives you three humps. Let's call first hump "-b", what comes next? (+/-) comes next. -b (+/-) the next term. So since we have one hump iterating, we have one hump joined to a positive and negative next hump. And that's bifurcation. That's literally the image you keep showing. And this also relates to transcendental numbers, which always come back up. The crazy thing is that transcendental numbers are an uncountably large infinite series of numbers.

Okay we have now 8 billion people on earth and it's still growing not settling down

I need boy friend

Bad arab. You missed a spelling point.

2020 is chaotic enough, but this man is smart.

I wish this guy was my teacher

How can I use this to win the Lotto? Thanks!

3:27 AM Me: hunched over the sink My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!

At least change the words to make it look original and not copy pasted

Sorry, you humans were not supposed to have stumbled upon this. Please wait while we update your server with a new patch, thank you for your patience -Robot Overlords

Fantastic! A masterpiece. This is my favorite video among all the ones I have watched so far. I felt like researching it in more detail, but for lack of time could not do it. My favorite moment is when you wonder about the mistery of the constant..Why that value? Are we ever know enough to answer those question. Veritassium at his best! Excellent material for the classroom.

Wow.

This is literally the equation to why we have periods in our life where everything seems to be going smoothly and then chaotic. Anytime there's a consonant ratio between the values, you experience harmony; vice versa, anytime there's a dissonant ratio between the values, we experience chaos. There's also proof of this in the way we hear music, interestingly. If I were to record myself hitting a drum (tuned to any frequency) and then play it rapidly, I can make a constant stream of notes. If I speed it up fast enough, you begin to hear it sound like a vibration. Faster than that and it creates a note based on how fast or slow it's played. Is this feeling freaky yet? Imagine now adding another drum playing alongside the preexisting drum with another constant stream of notes. In the space it takes the 1st drummer to play 2 notes, the other is playing 3 giving us a 3:2 ratio. Speed these up together and we begin to hear an interval of a perfect 5th between the two notes. There is no limit to # of ratios (hemiolas). Once you add another player, there are now 3 notes heard and harmony is formed. So mathematically, percussionists make the world go 'round.

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