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

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 馃檶
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.
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: "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4" "Busy World" "Children of Mystery"


  • Random X
    Random X5 godzin temu

    How do you guys come up with such things.

  • Connor Eyer
    Connor Eyer5 godzin temu

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

  • troeteimarsch
    troeteimarsch7 godzin temu

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

  • Chris Incorvati
    Chris Incorvati8 godzin temu

    Order begets chaos, chaos begets order.

  • Zygorg
    Zygorg8 godzin temu

    You adquired a new tittle: Chaotic (Neutral)

  • Carlos Handojo Santosa
    Carlos Handojo Santosa10 godzin temu

    You just blew my mind.

  • Holyfield Barrett
    Holyfield Barrett11 godzin temu

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

  • GrandAdmiral Zod
    GrandAdmiral Zod12 godzin temu

    The anti-life/death equation?

  • 銉┿偆銈€兂
    銉┿偆銈€兂12 godzin temu

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

  • reckless bose
    reckless bose13 godzin temu

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

  • Maeby Moore
    Maeby Moore13 godzin temu

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

  • Beulah West
    Beulah West13 godzin temu

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  • Brittany Baker
    Brittany Baker13 godzin temu

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  • RealJustinCase
    RealJustinCase14 godzin temu

    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 X15 godzin temu

    Chaos is so subjective

  • Shoedi L
    Shoedi L17 godzin temu

    Overpopulation debukned.

    USNBRENDON17 godzin temu

    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 S谩nchez de I帽igo
    Manuel S谩nchez de I帽igo17 godzin temu

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

  • Scispace Facts
    Scispace Facts23 godzin temu


  • Abdullah Bham
    Abdullah BhamDzie艅 temu

    Design God

  • John Dalzell
    John DalzellDzie艅 temu

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

  • tylor anderson
    tylor andersonDzie艅 temu

    When I say chaos, you say fogginbom, chaos

  • Mad Maniac
    Mad ManiacDzie艅 temu

    I didnt understand anything

  • mark ryan Jervoso
    mark ryan JervosoDzie艅 temu

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

  • naysay02
    naysay02Dzie艅 temu

    These numbers are living things. This is extraordinary.

  • Olli Bruno
    Olli BrunoDzie艅 temu

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

  • Kryptonicul
    KryptoniculDzie艅 temu

    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 PUBGMDzie艅 temu

    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.

  • Leif Schmit-Kallas
    Leif Schmit-KallasDzie艅 temu

    The correct name for a population of rabbits is Fluffle.

  • Basil Al-jaml
    Basil Al-jamlDzie艅 temu

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

  • pudpud kirkpatrick
    pudpud kirkpatrickDzie艅 temu

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  • Snow Ko Oo
    Snow Ko Oo2 dni temu

    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馃槣

  • Cerberus
    Cerberus2 dni temu

    4.669 hehehe funny number.

  • Jonas Fermefors
    Jonas Fermefors2 dni temu

    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 Zutzut2 dni temu

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

  • Axel From Group Therapy
    Axel From Group Therapy2 dni temu

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

  • Shark Falcon
    Shark Falcon2 dni temu

    Amazing science communicator. Heads of to you sir!

  • Jack Barbey
    Jack Barbey2 dni temu

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

  • O Riddle
    O Riddle2 dni temu

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

  • Brian Segovia
    Brian Segovia2 dni temu

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  • Marc030320
    Marc0303202 dni temu

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

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    鞙犾湢氤错槃2 dni temu

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

  • Emily uwu
    Emily uwu3 dni temu

    I gave up 1:35 in 馃ゲ

  • Hola Como Estas
    Hola Como Estas3 dni temu

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    Esther Cook3 dni temu

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  • Tommaso D'Este
    Tommaso D'Este3 dni temu

    Nice video

  • Kouzoulos14
    Kouzoulos143 dni temu

    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

  • Kouzoulos14


    Dzie艅 temu

    @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


    Dzie艅 temu

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

  • Digota
    Digota3 dni temu

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

  • Orion Nash
    Orion Nash3 dni temu

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

  • Greggy Dy
    Greggy Dy3 dni temu

    you lost me at 鈥淭his one simple eQUaTioN鈥

  • Lcx
    Lcx3 dni temu

    should i understand this video?! :)

  • Jason Spades
    Jason Spades3 dni temu

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

  • Camilo Delgado
    Camilo Delgado3 dni temu

    0:58 the video ended for me

  • pravin rao
    pravin rao3 dni temu

    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 rao3 dni temu

    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

    3 dni temu

    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

    3 dni temu

    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 rao3 dni temu

    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
    Juseman3 dni temu

    If my girlfriend was an equation.

  • Dreaming One
    Dreaming One3 dni temu

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

  • Jose Medina
    Jose Medina3 dni temu

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  • Error 10110
    Error 101103 dni temu


  • Jasper Ecb
    Jasper Ecb3 dni temu

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  • FollowIfYouSwallow
    FollowIfYouSwallow3 dni temu

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

  • Stefan Papdi
    Stefan Papdi3 dni temu

    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 Luz3 dni temu

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

  • Diego Mo
    Diego Mo3 dni temu

    Cool hyper dimensional Pringle you got there

  • Dan iel
    Dan iel3 dni temu

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

  • Ed Garzaro
    Ed Garzaro3 dni temu

    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.

  • mario yu
    mario yu3 dni temu

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  • Ismail Moufid
    Ismail Moufid4 dni temu

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

  • Aayush
    Aayush4 dni temu

    Nyc Trick: 2:14

  • Toon Vd Wielen
    Toon Vd Wielen4 dni temu

    Thanks man

  • DevilCouldCare
    DevilCouldCare4 dni temu

    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).

  • Donnie Baker
    Donnie Baker4 dni temu

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  • Andrew Thomas
    Andrew Thomas4 dni temu

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

  • Willy Madison
    Willy Madison4 dni temu

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  • Flip More
    Flip More4 dni temu

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

  • Alberto Hidalgo
    Alberto Hidalgo4 dni temu

    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 _osu4 dni temu

    *y = mx + b has entered the chat*

  • Tom Georg Eriksen
    Tom Georg Eriksen4 dni temu

    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 Mason4 dni temu

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

  • Nicolas
    Nicolas4 dni temu

    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 iPad4 dni temu

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

  • Makyr


    2 dni temu

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

  • Evatan
    Evatan4 dni temu

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

  • Harryboi 64
    Harryboi 645 dni temu

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

  • Kylie Nelson

    Kylie Nelson

    4 dni temu

    Same lol

  • Akilesh
    Akilesh5 dni temu

    I read about this in Nonlinear Dynamics

  • Steven Eaton
    Steven Eaton5 dni temu

    The answer to the question is CERN.

  • gia
    gia5 dni temu

    i. understand

  • Aditya Kishore
    Aditya Kishore5 dni temu

    This is what feels like after death

  • Oruga Margo
    Oruga Margo5 dni temu


  • Elnora Winn
    Elnora Winn5 dni temu

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  • Charge0Complete
    Charge0Complete5 dni temu

    OMG...the camera man or woman is a vampire or vampiress

  • 銇裤伩銇峆 official
    銇裤伩銇峆 official5 dni temu

    this guy is the madest scientist ever

  • 65 - Sebastian Fretes
    65 - Sebastian Fretes5 dni temu

    i can`t stop thinking of epicnpcman`s fisherman.... (help)

  • A L
    A L5 dni temu

    So many equations and models that repeat throughout life. Almost like it was programmed that way.

  • Fernando Mtlvo
    Fernando Mtlvo5 dni temu

    11:40 heartbeat pulse????

  • Rob
    Rob6 dni temu


  • Marko
    Marko6 dni temu

    鈥淭oday's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. 鈥 鈥 Nikola Tesla.

  • DomiNickel
    DomiNickel6 dni temu

    good video

  • Nebuchadnezzar Quellcris
    Nebuchadnezzar Quellcris6 dni temu

    There should be a completely different field called the Mathematics of Nature. It's fascinating

  • Native


    3 dni temu

    Mathematics itself is already nature. Why is this so hard for people to grasp? Is this forbidden knowledge? Lol

  • Pirkulator _

    Pirkulator _

    4 dni temu

    鈥淎pplied鈥 usually implies that, For future reference.

  • Jeremy Delgado
    Jeremy Delgado6 dni temu

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