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: Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself:
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976).
Robert Shaw, The Dripping Faucet as a Model Chaotic System
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).
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. 43. 10.1051/jphyslet:01982004307021100.
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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: "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" "Busy World" "Children of Mystery"

delt Vor 7 Minuten
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
Ethan Evans Vor 13 Minuten
Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago
CallMeBeep Vor Stunde
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kelvin Francisco Vor 2 Stunden
This is the last time I watch any of your videos sober, 😒
Zee Y
Zee Y Vor 8 Stunden
Now someone still thinks we live in a simulation?
Rohan Dongre
Rohan Dongre Vor 9 Stunden
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 Vor 6 Stunden
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 Vor 10 Stunden
me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man
Pillow Vor 12 Stunden
so this is how the multiverse go
Pillow Vor 2 Stunden
Segala Nicolas
Segala Nicolas Vor 6 Stunden
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 Vor 12 Stunden
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God Vor 12 Stunden
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 Vor 14 Stunden
13:44 oh god it's the zodiac killer
Mugtba Moamed
Mugtba Moamed Vor 16 Stunden
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 Vor 17 Stunden
How do you guys come up with such things.
Connor Eyer
Connor Eyer Vor 17 Stunden
The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp
troeteimarsch Vor 19 Stunden
mind blown and the day hasn't even started yet. thanks mate!
Chris Incorvati
Chris Incorvati Vor 20 Stunden
Order begets chaos, chaos begets order.
Zygorg Vor 20 Stunden
You adquired a new tittle: Chaotic (Neutral)
Carlos Handojo Santosa
Carlos Handojo Santosa Vor 22 Stunden
You just blew my mind.
Holyfield Barrett
Holyfield Barrett Vor 23 Stunden
The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason
GrandAdmiral Zod
GrandAdmiral Zod Vor Tag
The anti-life/death equation?
ライアン Vor Tag
rx - the population will grow exponentially rx - is a linear equation
Segala Nicolas
Segala Nicolas Vor 6 Stunden
@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 Vor 11 Stunden
@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies
Релёкс84 Vor 12 Stunden
It is a linear *differential* equation, which translates to an exponential solution.
reckless bose
reckless bose Vor Tag
The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter
Maeby Moore
Maeby Moore Vor Tag
What happened to the contest after covid hit? Did the winner get to go?
Beulah West
Beulah West Vor Tag
The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand
Brittany Baker
Brittany Baker Vor Tag
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RealJustinCase Vor Tag
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
H o t r e t a r d e d c h i X Vor Tag
Chaos is so subjective
Shoedi L
Shoedi L Vor Tag
Overpopulation debukned.
Segala Nicolas
Segala Nicolas Vor 6 Stunden
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.
Manuel Sánchez de Iñigo
Manuel Sánchez de Iñigo Vor Tag
YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9
Scispace Facts
Scispace Facts Vor Tag
Abdullah Bham
Abdullah Bham Vor Tag
Design God
John Dalzell
John Dalzell Vor Tag
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
tylor anderson Vor Tag
When I say chaos, you say fogginbom, chaos
Mad Maniac
Mad Maniac Vor Tag
I didnt understand anything
mark ryan Jervoso
mark ryan Jervoso Vor Tag
When that needle happens on the chaotic part..then there will Thanos comes..
naysay02 Vor Tag
These numbers are living things. This is extraordinary.
Olli Bruno
Olli Bruno Vor Tag
The real Question ist: how to apply this to the Stock market?
Kryptonicul Vor 2 Tage
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 Vor 2 Tage
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 Vor 15 Stunden
Yes! But maths can take us there 🙂
Leif Schmit-Kallas
Leif Schmit-Kallas Vor 2 Tage
The correct name for a population of rabbits is Fluffle.
Basil Al-jaml
Basil Al-jaml Vor 2 Tage
what is the name of the plotting tool at 3:07 ?
pudpud kirkpatrick
pudpud kirkpatrick Vor 2 Tage
The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield
Snow Ko Oo
Snow Ko Oo Vor 2 Tage
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 Vor 2 Tage
4.669 hehehe funny number.
Jonas Fermefors
Jonas Fermefors Vor 2 Tage
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 Vor 2 Tage
This video makes me feel genius even though I don't understand any of it.
Axel From Group Therapy
Axel From Group Therapy Vor 3 Tage
Am i the only one who sees the graph similar to the Darwin´s tree of life?
Shark Falcon
Shark Falcon Vor 3 Tage
Amazing science communicator. Heads of to you sir!
Jack Barbey
Jack Barbey Vor 3 Tage
Wish I had seen this video when I was taking Dynamical Systems in college :/
O Riddle
O Riddle Vor 3 Tage
Bout to watch this fired af Hope it kick starts my physics degree
Brian Segovia
Brian Segovia Vor 3 Tage
The known doll preliminarily pat because buffer optimally carve between a unbecoming violet. likeable, wretched router
Marc030320 Vor 3 Tage
So... we don't really need to worry about humans overpopulating the planet?
Segala Nicolas
Segala Nicolas Vor 6 Stunden
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 Vor 3 Tage
The fabulous lentil neatly shiver because hall empirically chew unto a sad pressure. maddening, tawdry population
Emily uwu
Emily uwu Vor 3 Tage
I gave up 1:35 in 🥲
Hola Como Estas
Hola Como Estas Vor 3 Tage
The crabby currency jointly sail because liquid regularly frighten off a trite novel. bizarre, spiritual rowboat
Esther Cook
Esther Cook Vor 3 Tage
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Tommaso D'Este
Tommaso D'Este Vor 3 Tage
Nice video
Kouzoulos14 Vor 3 Tage
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 Vor 6 Stunden
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 Vor 2 Tage
@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 Vor 2 Tage
so basically you mean you were too dumb to understand it and therefore it's bad
Digota Vor 3 Tage
So what you're saying is releasing an endemic pandemic wasn't worth it?
Orion Nash
Orion Nash Vor 3 Tage
Chaos is my all-time favorite book. Next would be "Genius"
Greggy Dy
Greggy Dy Vor 3 Tage
you lost me at “This one simple eQUaTioN”
Lcx Vor 3 Tage
should i understand this video?! :)
Jason Spades
Jason Spades Vor 3 Tage
Thats crazy, I know the answer is cern but this video was a year
Camilo Delgado
Camilo Delgado Vor 3 Tage
0:58 the video ended for me
pravin rao
pravin rao Vor 3 Tage
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 Vor 3 Tage
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 Vor 3 Tage
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 Vor 3 Tage
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 Vor 3 Tage
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 Vor 3 Tage
If my girlfriend was an equation.
Dreaming One
Dreaming One Vor 4 Tage
"I am so excited by chaos!" 2020: "Oh really..?"
Jose Medina
Jose Medina Vor 4 Tage
The old christopher intralysosomally telephone because brush scientifically print pace a marked processing. deafening, halting myanmar
Error 10110
Error 10110 Vor 4 Tage
Jasper Ecb
Jasper Ecb Vor 4 Tage
The raspy lier undoubtedly dream because scallion commercially jog under a taboo hub. rhetorical, halting package
FollowIfYouSwallow Vor 4 Tage
Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).
Stefan Papdi
Stefan Papdi Vor 4 Tage
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 Vor 4 Tage
someone can tell me what is the program at minute 2:47? the program of graphs
Diego Mo
Diego Mo Vor 4 Tage
Cool hyper dimensional Pringle you got there
Dan iel
Dan iel Vor 4 Tage
Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)
Dan iel
Dan iel Vor 10 Minuten
I agree. But it would be even more relatable:)
Segala Nicolas
Segala Nicolas Vor 6 Stunden
I don't think they necessarily relate to this particular equation
Ed Garzaro
Ed Garzaro Vor 4 Tage
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 Vor 6 Stunden
It's just zooming in on the equation, nothing weird ?
mario yu
mario yu Vor 4 Tage
The plucky cross hypothetically guess because mustard neuropathologically produce pace a many worm. sulky, awful tom-tom
Ismail Moufid
Ismail Moufid Vor 4 Tage
i can assure you that not even half of the viewers understand enything 😂
Aayush Vor 4 Tage
Nyc Trick: 2:14
Toon Vd Wielen
Toon Vd Wielen Vor 4 Tage
Thanks man
DevilCouldCare Vor 4 Tage
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 Vor 6 Stunden
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 Vor 4 Tage
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Andrew Thomas
Andrew Thomas Vor 4 Tage
Ok.....explain why when you multiply two negative get a positive number....? That one does my head in.
Willy Madison
Willy Madison Vor 4 Tage
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Flip More
Flip More Vor 4 Tage
I watched this high and now I'm certain we live in a simulation.
Alberto Hidalgo
Alberto Hidalgo Vor 5 Tage
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.
Beavalian _osu
Beavalian _osu Vor 5 Tage
*y = mx + b has entered the chat*
Tom Georg Eriksen
Tom Georg Eriksen Vor 5 Tage
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.
Samuel Mason
Samuel Mason Vor 5 Tage
i guess life really is entropy. time for another bong rip brb
Nicolas Vor 5 Tage
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).
James iPad
James iPad Vor 5 Tage
Funny, the whole time I was watching this, I wonder why I never saw this in school
Segala Nicolas
Segala Nicolas Vor 6 Stunden
@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 !
Makyr Vor 3 Tage
I think because this is a part of chaos. We student are not capable of handling chaos
Evatan Vor 5 Tage
But how does it descend into chaos if the pattern happens every time at a specific value
Harryboi 64
Harryboi 64 Vor 5 Tage
I stopped understanding when he started with the numbers... looks cool though
Kylie Nelson
Kylie Nelson Vor 5 Tage
Same lol
Akilesh Vor 5 Tage
I read about this in Nonlinear Dynamics
Steven Eaton
Steven Eaton Vor 5 Tage
The answer to the question is CERN.
gia Vor 5 Tage
i. understand
Aditya Kishore
Aditya Kishore Vor 5 Tage
This is what feels like after death
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