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"

29 jan 2020

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Betsy Larcom Pirms 40 Minūtes

I was an ecology major in undergrad and everyone else thought we just went around hugging trees...

Bare Bear Hands Pirms Stundas

Chaos is natural order.

Eric Swenson Pirms 6 Stundām

And no one thinks there is a creator that did all this by design? All these links and ratios no one can explain the existence of, and we think it all just came about by accident...

Rohit Neemwal Pirms 7 Stundām

so random numbers are not so random.

Rohit Neemwal Pirms 7 Stundām

universal constants are just some values given to simulator to simulate our universe.hece we are in simulator

Rohit Neemwal Pirms 7 Stundām

so , we are in simulation .

Steven Pirms 7 Stundām

The mandelbrook fractal looks lika a turtle:)

Vinyas Singh Pirms 9 Stundām

I guess the made up/unexplained answer of "42" we get to hear about has something to do with this universal constant of "4.669", I'm not sure though.

Xer R Pirms 10 Stundām

You should make a podcast

O Templo de Shaka Pirms 12 Stundām

I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.

Hein Htet Pirms 13 Stundām

There is no chaos. Everything has a pattern at certain perspective.

Martin Da Monarch Pirms 14 Stundām

That kinda looks like how a tree 🌳 grows lol cool

delt Pirms 21 Stundas

Seeeeriously fascinating!!!! 😲😲

Ethan Evans Pirms 21 Stundas

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

CallMeBeep Pirms 23 Stundām

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

Kelvin Francisco Pirms 23 Stundām

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

Zee Y Pirms dienas

Now someone still thinks we live in a simulation?

Rohan Dongre Pirms dienas

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.

Segala Nicolas Pirms dienas

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.

bereket taffesse Pirms dienas

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

Pillow Pirms dienas

so this is how the multiverse go

Pillow Pirms 23 Stundām

multiverse

Segala Nicolas Pirms dienas

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

Michael Pirms dienas

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

God Pirms dienas

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

Fractal Pirms dienas

13:44 oh god it's the zodiac killer

Mugtba Moamed Pirms dienas

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

Random X Pirms dienas

How do you guys come up with such things.

Connor Eyer Pirms dienas

The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp

troeteimarsch Pirms dienas

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

Chris Incorvati Pirms dienas

Order begets chaos, chaos begets order.

Zygorg Pirms dienas

You adquired a new tittle: Chaotic (Neutral)

Carlos Handojo Santosa Pirms dienas

You just blew my mind.

Holyfield Barrett Pirms dienas

The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason

GrandAdmiral Zod Pirms dienas

The anti-life/death equation?

ライアン Pirms dienas

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

Segala Nicolas Pirms dienas

@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

ライアン Pirms dienas

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

Релёкс84 Pirms dienas

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

reckless bose Pirms dienas

The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter

Maeby Moore Pirms dienas

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

Beulah West Pirms dienas

The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand

Brittany Baker Pirms dienas

The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year

RealJustinCase Pirms dienas

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

H o t r e t a r d e d c h i X Pirms 2 dienām

Chaos is so subjective

Shoedi L Pirms 2 dienām

Overpopulation debukned.

Segala Nicolas Pirms dienas

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

USNBRENDON Pirms 2 dienām

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.

Manuel Sánchez de Iñigo Pirms 2 dienām

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

Scispace Facts Pirms 2 dienām

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

Abdullah Bham Pirms 2 dienām

Design ..by God

John Dalzell Pirms 2 dienām

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

tylor anderson Pirms 2 dienām

When I say chaos, you say fogginbom, chaos

Mad Maniac Pirms 2 dienām

I didnt understand anything

mark ryan Jervoso Pirms 2 dienām

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

naysay02 Pirms 2 dienām

These numbers are living things. This is extraordinary.

Olli Bruno Pirms 2 dienām

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

Kryptonicul Pirms 2 dienām

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"

Manners PUBGM Pirms 2 dienām

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.

Kim-André Johansen Pirms dienas

Yes! But maths can take us there 🙂

Leif Schmit-Kallas Pirms 3 dienām

The correct name for a population of rabbits is Fluffle.

Basil Al-jaml Pirms 3 dienām

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

pudpud kirkpatrick Pirms 3 dienām

The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield

Snow Ko Oo Pirms 3 dienām

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😜

Cerberus Pirms 3 dienām

4.669 hehehe funny number.

Jonas Fermefors Pirms 3 dienām

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.

Enzhou Zutzut Pirms 3 dienām

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

Axel From Group Therapy Pirms 3 dienām

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

Shark Falcon Pirms 4 dienām

Amazing science communicator. Heads of to you sir!

Jack Barbey Pirms 4 dienām

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

O Riddle Pirms 4 dienām

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

Brian Segovia Pirms 4 dienām

The known doll preliminarily pat because buffer optimally carve between a unbecoming violet. likeable, wretched router

Marc030320 Pirms 4 dienām

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

Segala Nicolas Pirms dienas

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 ?

유유보현 Pirms 4 dienām

The fabulous lentil neatly shiver because hall empirically chew unto a sad pressure. maddening, tawdry population

Emily uwu Pirms 4 dienām

I gave up 1:35 in 🥲

Hola Como Estas Pirms 4 dienām

The crabby currency jointly sail because liquid regularly frighten off a trite novel. bizarre, spiritual rowboat

Esther Cook Pirms 4 dienām

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Tommaso D'Este Pirms 4 dienām

Nice video

Kouzoulos14 Pirms 4 dienām

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

Segala Nicolas Pirms dienas

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.

Kouzoulos14 Pirms 3 dienām

@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

Vad3r Pirms 3 dienām

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

Digota Pirms 4 dienām

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

Orion Nash Pirms 4 dienām

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

Greggy Dy Pirms 4 dienām

you lost me at “This one simple eQUaTioN”

Lcx Pirms 4 dienām

should i understand this video?! :)

Jason Spades Pirms 4 dienām

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

Camilo Delgado Pirms 4 dienām

0:58 the video ended for me

pravin rao Pirms 4 dienām

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

pravin rao Pirms 4 dienām

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.

pravin rao Pirms 4 dienām

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.

pravin rao Pirms 4 dienām

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

pravin rao Pirms 4 dienām

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

Juseman Pirms 4 dienām

If my girlfriend was an equation.

Dreaming One Pirms 4 dienām

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

Jose Medina Pirms 4 dienām

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Error 10110 Pirms 4 dienām

Wut?

Jasper Ecb Pirms 5 dienām

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FollowIfYouSwallow Pirms 5 dienām

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

Stefan Papdi Pirms 5 dienām

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

Derek Da Luz Pirms 5 dienām

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

Diego Mo Pirms 5 dienām

Cool hyper dimensional Pringle you got there

Dan iel Pirms 5 dienām

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

Dan iel Pirms 21 Stundas

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

Segala Nicolas Pirms dienas

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

Ed Garzaro Pirms 5 dienām

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.

Segala Nicolas Pirms dienas

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

mario yu Pirms 5 dienām

The plucky cross hypothetically guess because mustard neuropathologically produce pace a many worm. sulky, awful tom-tom

Ismail Moufid Pirms 5 dienām

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

Aayush Pirms 5 dienām

Nyc Trick: 2:14

Toon Vd Wielen Pirms 5 dienām

Thanks man

DevilCouldCare Pirms 5 dienām

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).

Segala Nicolas Pirms dienas

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

Donnie Baker Pirms 5 dienām

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Andrew Thomas Pirms 5 dienām

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

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Flip More Pirms 5 dienām

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

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