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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:

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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"

Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago

Did you upload the vid ultra-wide just for me? :D

This is the last time I watch any of your videos sober, 😒

Now someone still thinks we live in a simulation?

What kind of math is that?? Initially you said X is no. of rabbits, then you choose X=0.4, how's that possible?? Now, if R is the rate of growth, population next year isn't X*R, but X*(1+R). Further if suggest that the rate of growth will depend on the present population, the R, for any year, will be expressed as a function of (Ps, Pp) where Ps is the saturation population assuming limited resources and Pp is the present population for that particular year. Therefore, Xn=RX(1-X) is incorrect.

The X is the percentage of population the theoretical maximum of the population. It makes sense to choose it arbitrarily, since what we care about is the value of X when it stabilises. And it will stabilise to the same value whether we choose it to be 0.4 or 0.9 or anything between 0 and 1. And secondly, it does make sense to multiply by the growth rate, as it makes an exponential model. The math here has been established since the 1970s, there are papers on this, of course it's correct.

me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man

so this is how the multiverse go

multiverse

No, this has nothing to do with that. But if you want something that feels like the multiverse, you should check out Veritasium's video on the Many Worlds theory of physics

Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.

THATS RIGHT!!! OH this got me so excited! :) Apply it to the cosmos and when a star releases energy to its surrounding planets. Chaos , adaptation to environment, then order but it evolves and branches out. The law of life. So many layers lol

13:44 oh god it's the zodiac killer

Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.

How do you guys come up with such things.

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mind blown and the day hasn't even started yet. thanks mate!

Order begets chaos, chaos begets order.

You adquired a new tittle: Chaotic (Neutral)

You just blew my mind.

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The anti-life/death equation?

rx - the population will grow exponentially rx - is a linear equation

@ライアン but it is exponential, because x(n+1)=r*x(n) is equivalent to x(n)=r^n so it's an exponential model because it's raised to a power. Anyway, the math here is correct

@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies

It is a linear *differential* equation, which translates to an exponential solution.

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What happened to the contest after covid hit? Did the winner get to go?

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I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself

Chaos is so subjective

Overpopulation debukned.

What do you mean ? That's not the point of the video, and I'm not sure what there is to debunk about overpopulation

CERN. August 1991. I believe it was few 6th.... But, yes, it was Switzerland's CERN that quietly switched on the first research website in the aim of studying particle based physics--atom smashing! Love it.

YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9

RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc

Design ..by God

I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.

When I say chaos, you say fogginbom, chaos

I didnt understand anything

When that needle happens on the chaotic part..then there will Thanos comes..

These numbers are living things. This is extraordinary.

The real Question ist: how to apply this to the Stock market?

Am i the only whos life is actually being changed by this stuff?? Its the only thing i can think about like all different types of infinity. Usually when im doing any task in my daily life ill spring into action or rather my brain does and starts think about how something can be infinite or is it infinite or can it be connected to infinity. The worst case of this is so simple but its almost hindering me, almost every two minutes in math class my brain just spits out "theres infinite amount of numbers in between ___ and ___" or "if you keep using that equation it will go for infinity" or even sometimes i try to make an infinite something like writing how many zeros after 0.0 before running out of room and having to put a 1 at the end. Tomorrow or maybe monday in class im going to use the mandelbrot equation to try and draw a small taste of a man made mandbrot set. Although I know I will be restricted by how much room I have on the page or whatever im drawing on. I almost feel restricted by reality or something. Considering everyone has ever told me that infinity is impossible to comprehend I seriously want to comprehend it or hear it or see it or just do anything that i could actually interact my sense with infinity. Of coure this will never happen considering there is no real infinity or at least not that we can "comprehend"

The only reason we call it chaos is because in order to see the chaos as a constant you would need to be in a higher dimension.

Yes! But maths can take us there 🙂

The correct name for a population of rabbits is Fluffle.

what is the name of the plotting tool at 3:07 ?

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click on the video Panik : Oh god , i am so dumb, i will not be able to change the view on the world Pause the video and.. click on comment section Kalm: yhh at least....i know i am not aloooone😜

4.669 hehehe funny number.

I haven't thought about Mandelbrot sets since I was 20 and they delivered the coolest graphics on the new VGA-card. The Mandelbrot set already has something organic about it, but this takes it to a new level: the actual underpinnings of the universe. The clickbait-like title was true. Blew my mind.

This video makes me feel genius even though I don't understand any of it.

Am i the only one who sees the graph similar to the Darwin´s tree of life?

Amazing science communicator. Heads of to you sir!

Wish I had seen this video when I was taking Dynamical Systems in college :/

Bout to watch this fired af Hope it kick starts my physics degree

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So... we don't really need to worry about humans overpopulating the planet?

In a sense, we don't : the population will reach and equilibrium, when the richest people will be able to afford the few resources that are left, and all the poor people will die. There will be less people, and the remaining people will be able to survive. But is that what we want ?

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I gave up 1:35 in 🥲

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Nice video

You may know a lot about Math, Physics etc... But this video doesn't really "change how people see the world". Not for the vast majority anyway. To achieve that, it needs to be simplified and shown. Sadly, none of these happened. Good luck with your future videos

You missed the point : the video can't be boiled down to its title ! You should rather listen to he conclusion, where he says that he wants to teach people about interesting things like chaos, and that will make a few more people engage with and be interested in math. And judging by the number of views, he achieved that goal.

@Vad3r from ur answer it seems tht u are too dumb to even understand what i m saying... me, the "dumb". have a great day/night all of u

so basically you mean you were too dumb to understand it and therefore it's bad

So what you're saying is releasing an endemic pandemic wasn't worth it?

Chaos is my all-time favorite book. Next would be "Genius"

you lost me at “This one simple eQUaTioN”

should i understand this video?! :)

Thats crazy, I know the answer is cern but this video was a year ago..lol

0:58 the video ended for me

Dude one flaw though. at r>=4 the equation will break and return negative values(eventually)[well it may show very quickly or a lot later]. Why did you not show that. I mean if complex numbers are real then it returning negatives values might also mean something intutive about our world. Ok genuine question though. When it returns negative values is it still cyclic or it completely breaks and goes near infinity. Never mind. Opened calculator it goes near negative infinity. Though ok is there a way to make it repeat while it is still negative. Like maybe it has some repetition in negative numbers too. What if we use complex numbers in the equations

Ok I am in highschool but i am pretty sure calling it fundamental constant of nature feels wrong. I think we can make equations and systems which take there previous state as input for there current state (and do anything) and get different constant. Just intuition i don't know anything. but it feels like you can relate previous thing to next thing and get constant. no wait though. Why would it be a constant then. If you are randomly relating stuff why should it be a constant.

Iterate it the way we have. So like you mean if we take previous value as input for the next value. So if single hump. Then no matter what we do. Ok what if i define a completely weird non algebraic function . Like without squares or multiplication . Will that work too. Ok though sin(x) can actually be written as a algebraic polynomial cause of Taylor series. So well anything can be written as that if we use Taylor series. Maybe something with polynomials. What if we use something which can't be approximated using Taylor series. WHAT IF WE USE A DERIVATIVE WHICH DON'T HAVE A ANTI DERIVATIVE. TO MAKE A FUNCTION(by manually computing that function on computer . ) LIKE WE CAN'T FIND A NEAT LITTLE FORMULA FOR IT IF THERE IS NO ANTI DERIVATIVE. WILL THE CONSTANT STILL EMERGE IF THERE IS A SINGLE HUMP. though what does similar mean does it just mean that new value is function of previous value.

15:30 huh that's pretty weird. Then it might actually be constant of nature or something. something is converging i think somewhere . Like something averages out somehow

Ok just watch 3lbue1browns video on complex numbers and you would understand it. Z (n+1) =Z (n)^2 +C Squaring complex is just rotating it by doubling it's angle and it's magnitude is squared. the C we add act's like subtraction probably from the total magnitude of complex number . So it just keeps rotating and getting subtracted perodically

If my girlfriend was an equation.

"I am so excited by chaos!" 2020: "Oh really..?"

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Wut?

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Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).

chaos knight in dota has varying critacal dmg (from 1.2-2.8) and lifesteal (20-120%) but i also am 23 and never heard of the particular constant 4.669

someone can tell me what is the program at minute 2:47? the program of graphs

Cool hyper dimensional Pringle you got there

Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)

I agree. But it would be even more relatable:)

I don't think they necessarily relate to this particular equation

Can you explain what is happening at 0:16 in your video? It's right after the equation appears and before you start speaking. Am I crazy, or does the environment suddenly look different and then suddenly normal.

It's just zooming in on the equation, nothing weird ?

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i can assure you that not even half of the viewers understand enything 😂

Nyc Trick: 2:14

Thanks man

Fantastic video. The section where the parabola is hand-drawn and the numbers punched into a calculator could have been substituted with a graphic showing how the height of the parabola is determined by r, and, how successive values are obtained by using the last y as the next x (reflected on the line y=x).

I prefer the way it was presented in the video because it helps with the intuition of iteration. It helps people understand the meaning of an iterative equation, and the meaning of a negative feedback loop

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Ok.....explain why when you multiply two negative numbers...you get a positive number....? That one does my head in.

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I watched this high and now I'm certain we live in a simulation.

when we give full confidence and faith that we already knew these things as a baby knows Calculus or trig as the baby begins to walk. trust your abilities and doubt not.

*y = mx + b has entered the chat*

I played with this formula in a spreadsheet, and observed that with a carefully picked initial population of nx = (r-1)/r I could maintain balance with enormous grow rates.

i guess life really is entropy. time for another bong rip brb

Sorry I left. it started I could follow . Then , it took a Ph D. to follow . So.... Try the K.I.S.S. method ( Keep it simple stupid).

Funny, the whole time I was watching this, I wonder why I never saw this in school

@Makyr at the end he says that we should teach just a little bit of Chaos, to get students interested in math ! Maybe we can't handle it, but we should telle the students it exists, to keep them motivated to learn more !

I think because this is a part of chaos. We student are not capable of handling chaos

But how does it descend into chaos if the pattern happens every time at a specific value

I stopped understanding when he started with the numbers... looks cool though

Same lol

I read about this in Nonlinear Dynamics

The answer to the question is CERN.

i. understand

This is what feels like after death

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