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This equation will change how you see the world (the logistic map) 

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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"

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29 jan 2020

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komentāri 100   
Betsy Larcom
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
Bare Bear Hands Pirms Stundas
Chaos is natural order.
Eric Swenson
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
Rohit Neemwal Pirms 7 Stundām
so random numbers are not so random.
Rohit Neemwal
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
Rohit Neemwal Pirms 7 Stundām
so , we are in simulation .
Steven
Steven Pirms 7 Stundām
The mandelbrook fractal looks lika a turtle:)
Vinyas Singh
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
Xer R Pirms 10 Stundām
You should make a podcast
O Templo de Shaka
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
Hein Htet Pirms 13 Stundām
There is no chaos. Everything has a pattern at certain perspective.
Martin Da Monarch
Martin Da Monarch Pirms 14 Stundām
That kinda looks like how a tree 🌳 grows lol cool
delt
delt Pirms 21 Stundas
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
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
CallMeBeep Pirms 23 Stundām
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kelvin Francisco Pirms 23 Stundām
This is the last time I watch any of your videos sober, 😒
Zee Y
Zee Y Pirms dienas
Now someone still thinks we live in a simulation?
Rohan Dongre
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
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
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
Pillow Pirms dienas
so this is how the multiverse go
Pillow
Pillow Pirms 23 Stundām
multiverse
Segala Nicolas
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
Michael Pirms dienas
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God
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
Fractal Pirms dienas
13:44 oh god it's the zodiac killer
Mugtba Moamed
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
Random X Pirms dienas
How do you guys come up with such things.
Connor Eyer
Connor Eyer Pirms dienas
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troeteimarsch
troeteimarsch Pirms dienas
mind blown and the day hasn't even started yet. thanks mate!
Chris Incorvati
Chris Incorvati Pirms dienas
Order begets chaos, chaos begets order.
Zygorg
Zygorg Pirms dienas
You adquired a new tittle: Chaotic (Neutral)
Carlos Handojo Santosa
You just blew my mind.
Holyfield Barrett
Holyfield Barrett Pirms dienas
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GrandAdmiral Zod
GrandAdmiral Zod Pirms dienas
The anti-life/death equation?
ライアン
ライアン Pirms dienas
rx - the population will grow exponentially rx - is a linear equation
Segala Nicolas
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
ライアン Pirms dienas
@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies
Релёкс84
Релёкс84 Pirms dienas
It is a linear *differential* equation, which translates to an exponential solution.
reckless bose
reckless bose Pirms dienas
The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter
Maeby Moore
Maeby Moore Pirms dienas
What happened to the contest after covid hit? Did the winner get to go?
Beulah West
Beulah West Pirms dienas
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Brittany Baker
Brittany Baker Pirms dienas
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RealJustinCase
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
Chaos is so subjective
Shoedi L
Shoedi L Pirms 2 dienām
Overpopulation debukned.
Segala Nicolas
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
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
YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9
Scispace Facts
Scispace Facts Pirms 2 dienām
RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc
Abdullah Bham
Abdullah Bham Pirms 2 dienām
Design ..by God
John Dalzell
John Dalzell Pirms 2 dienām
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
tylor anderson Pirms 2 dienām
When I say chaos, you say fogginbom, chaos
Mad Maniac
Mad Maniac Pirms 2 dienām
I didnt understand anything
mark ryan Jervoso
mark ryan Jervoso Pirms 2 dienām
When that needle happens on the chaotic part..then there will Thanos comes..
naysay02
naysay02 Pirms 2 dienām
These numbers are living things. This is extraordinary.
Olli Bruno
Olli Bruno Pirms 2 dienām
The real Question ist: how to apply this to the Stock market?
Kryptonicul
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
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
Kim-André Johansen Pirms dienas
Yes! But maths can take us there 🙂
Leif Schmit-Kallas
Leif Schmit-Kallas Pirms 3 dienām
The correct name for a population of rabbits is Fluffle.
Basil Al-jaml
Basil Al-jaml Pirms 3 dienām
what is the name of the plotting tool at 3:07 ?
pudpud kirkpatrick
pudpud kirkpatrick Pirms 3 dienām
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Snow Ko Oo
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
Cerberus Pirms 3 dienām
4.669 hehehe funny number.
Jonas Fermefors
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
Enzhou Zutzut Pirms 3 dienām
This video makes me feel genius even though I don't understand any of it.
Axel From Group Therapy
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
Shark Falcon Pirms 4 dienām
Amazing science communicator. Heads of to you sir!
Jack Barbey
Jack Barbey Pirms 4 dienām
Wish I had seen this video when I was taking Dynamical Systems in college :/
O Riddle
O Riddle Pirms 4 dienām
Bout to watch this fired af Hope it kick starts my physics degree
Brian Segovia
Brian Segovia Pirms 4 dienām
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Marc030320
Marc030320 Pirms 4 dienām
So... we don't really need to worry about humans overpopulating the planet?
Segala Nicolas
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
유유보현 Pirms 4 dienām
The fabulous lentil neatly shiver because hall empirically chew unto a sad pressure. maddening, tawdry population
Emily uwu
Emily uwu Pirms 4 dienām
I gave up 1:35 in 🥲
Hola Como Estas
Hola Como Estas Pirms 4 dienām
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Esther Cook
Esther Cook Pirms 4 dienām
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Tommaso D'Este
Tommaso D'Este Pirms 4 dienām
Nice video
Kouzoulos14
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
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
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
Vad3r Pirms 3 dienām
so basically you mean you were too dumb to understand it and therefore it's bad
Digota
Digota Pirms 4 dienām
So what you're saying is releasing an endemic pandemic wasn't worth it?
Orion Nash
Orion Nash Pirms 4 dienām
Chaos is my all-time favorite book. Next would be "Genius"
Greggy Dy
Greggy Dy Pirms 4 dienām
you lost me at “This one simple eQUaTioN”
Lcx
Lcx Pirms 4 dienām
should i understand this video?! :)
Jason Spades
Jason Spades Pirms 4 dienām
Thats crazy, I know the answer is cern but this video was a year ago..lol
Camilo Delgado
Camilo Delgado Pirms 4 dienām
0:58 the video ended for me
pravin rao
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
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
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
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
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
Juseman Pirms 4 dienām
If my girlfriend was an equation.
Dreaming One
Dreaming One Pirms 4 dienām
"I am so excited by chaos!" 2020: "Oh really..?"
Jose Medina
Jose Medina Pirms 4 dienām
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Error 10110
Error 10110 Pirms 4 dienām
Wut?
Jasper Ecb
Jasper Ecb Pirms 5 dienām
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FollowIfYouSwallow
FollowIfYouSwallow Pirms 5 dienām
Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).
Stefan Papdi
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
Derek Da Luz Pirms 5 dienām
someone can tell me what is the program at minute 2:47? the program of graphs
Diego Mo
Diego Mo Pirms 5 dienām
Cool hyper dimensional Pringle you got there
Dan iel
Dan iel Pirms 5 dienām
Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)
Dan iel
Dan iel Pirms 21 Stundas
I agree. But it would be even more relatable:)
Segala Nicolas
Segala Nicolas Pirms dienas
I don't think they necessarily relate to this particular equation
Ed Garzaro
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
Segala Nicolas Pirms dienas
It's just zooming in on the equation, nothing weird ?
mario yu
mario yu Pirms 5 dienām
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Ismail Moufid
Ismail Moufid Pirms 5 dienām
i can assure you that not even half of the viewers understand enything 😂
Aayush
Aayush Pirms 5 dienām
Nyc Trick: 2:14
Toon Vd Wielen
Toon Vd Wielen Pirms 5 dienām
Thanks man
DevilCouldCare
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
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
Donnie Baker Pirms 5 dienām
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Andrew Thomas
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.
Willy Madison
Willy Madison Pirms 5 dienām
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Flip More
Flip More Pirms 5 dienām
I watched this high and now I'm certain we live in a simulation.
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