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

98 431 visningar 10mn

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.
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"


  1. korteks visceralzen
    korteks visceralzen
    4 timmar sedan

    Thanks. I love this channel. No one explains this stuff.

  2. Betsy Larcom
    Betsy Larcom
    9 timmar sedan

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

  3. Bare Bear Hands
    Bare Bear Hands
    9 timmar sedan

    Chaos is natural order.

  4. Eric Swenson
    Eric Swenson
    14 timmar sedan

    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...

  5. Rohit Neemwal
    Rohit Neemwal
    15 timmar sedan

    so random numbers are not so random.

  6. Rohit Neemwal
    Rohit Neemwal
    15 timmar sedan

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

  7. Rohit Neemwal
    Rohit Neemwal
    15 timmar sedan

    so , we are in simulation .

  8. Steven
    15 timmar sedan

    The mandelbrook fractal looks lika a turtle:)

  9. Vinyas Singh
    Vinyas Singh
    18 timmar sedan

    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.

  10. Xer R
    Xer R
    18 timmar sedan

    You should make a podcast

  11. O Templo de Shaka
    O Templo de Shaka
    21 timme sedan

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

  12. Hein Htet
    Hein Htet
    21 timme sedan

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

  13. Martin Da Monarch
    Martin Da Monarch
    23 timmar sedan

    That kinda looks like how a tree 🌳 grows lol cool

  14. delt
    Dag sedan

    Seeeeriously fascinating!!!! 😲😲

  15. Ethan Evans
    Ethan Evans
    Dag sedan

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

  16. CallMeBeep
    Dag sedan

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

  17. Kelvin Francisco
    Kelvin Francisco
    Dag sedan

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

  18. Zee Y
    Zee Y
    Dag sedan

    Now someone still thinks we live in a simulation?

  19. Rohan Dongre
    Rohan Dongre
    Dag sedan

    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.

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

      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.

  20. bereket taffesse
    bereket taffesse
    Dag sedan

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

  21. Pillow
    Dag sedan

    so this is how the multiverse go

    1. Pillow
      Dag sedan


    2. Segala Nicolas
      Segala Nicolas
      Dag sedan

      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

  22. Michael
    Dag sedan

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

  23. God
    Dag sedan

    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

  24. Fractal
    Dag sedan

    13:44 oh god it's the zodiac killer

  25. Mugtba Moamed
    Mugtba Moamed
    Dag sedan

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

  26. Random X
    Random X
    Dag sedan

    How do you guys come up with such things.

  27. Connor Eyer
    Connor Eyer
    Dag sedan

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  28. troeteimarsch
    2 dagar sedan

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

  29. Chris Incorvati
    Chris Incorvati
    2 dagar sedan

    Order begets chaos, chaos begets order.

  30. Zygorg
    2 dagar sedan

    You adquired a new tittle: Chaotic (Neutral)

  31. Carlos Handojo Santosa
    Carlos Handojo Santosa
    2 dagar sedan

    You just blew my mind.

  32. Holyfield Barrett
    Holyfield Barrett
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  33. GrandAdmiral Zod
    GrandAdmiral Zod
    2 dagar sedan

    The anti-life/death equation?

  34. ライアン
    2 dagar sedan

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

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

      @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

    2. ライアン
      Dag sedan

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

    3. Релёкс84
      Dag sedan

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

  35. reckless bose
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  36. Maeby Moore
    Maeby Moore
    2 dagar sedan

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

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  39. RealJustinCase
    2 dagar sedan

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

  40. 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
    2 dagar sedan

    Chaos is so subjective

  41. Shoedi L
    Shoedi L
    2 dagar sedan

    Overpopulation debukned.

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

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

    2 dagar sedan

    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.

  43. Manuel Sánchez de Iñigo
    Manuel Sánchez de Iñigo
    2 dagar sedan

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

  44. Scispace Facts
    Scispace Facts
    2 dagar sedan


  45. Abdullah Bham
    Abdullah Bham
    3 dagar sedan

    Design God

  46. John Dalzell
    John Dalzell
    3 dagar sedan

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

  47. tylor anderson
    tylor anderson
    3 dagar sedan

    When I say chaos, you say fogginbom, chaos

  48. Mad Maniac
    Mad Maniac
    3 dagar sedan

    I didnt understand anything

  49. mark ryan Jervoso
    mark ryan Jervoso
    3 dagar sedan

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

  50. naysay02
    3 dagar sedan

    These numbers are living things. This is extraordinary.

  51. Olli Bruno
    Olli Bruno
    3 dagar sedan

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

  52. Kryptonicul
    3 dagar sedan

    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"

  53. Manners PUBGM
    Manners PUBGM
    3 dagar sedan

    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.

    1. Kim-André Johansen
      Kim-André Johansen
      Dag sedan

      Yes! But maths can take us there 🙂

  54. Leif Schmit-Kallas
    Leif Schmit-Kallas
    3 dagar sedan

    The correct name for a population of rabbits is Fluffle.

  55. Basil Al-jaml
    Basil Al-jaml
    3 dagar sedan

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

  56. pudpud kirkpatrick
    pudpud kirkpatrick
    3 dagar sedan

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

  57. Snow Ko Oo
    Snow Ko Oo
    3 dagar sedan

    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😜

  58. Cerberus
    3 dagar sedan

    4.669 hehehe funny number.

  59. Jonas Fermefors
    Jonas Fermefors
    4 dagar sedan

    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.

  60. Enzhou Zutzut
    Enzhou Zutzut
    4 dagar sedan

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

  61. Axel From Group Therapy
    Axel From Group Therapy
    4 dagar sedan

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

  62. Shark Falcon
    Shark Falcon
    4 dagar sedan

    Amazing science communicator. Heads of to you sir!

  63. Jack Barbey
    Jack Barbey
    4 dagar sedan

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

  64. O Riddle
    O Riddle
    4 dagar sedan

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

  65. Brian Segovia
    Brian Segovia
    4 dagar sedan

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

  66. Marc030320
    4 dagar sedan

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

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

      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 ?

  67. 유유보현
    4 dagar sedan

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

  68. Emily uwu
    Emily uwu
    4 dagar sedan

    I gave up 1:35 in 🥲

  69. Hola Como Estas
    Hola Como Estas
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  71. Tommaso D'Este
    Tommaso D'Este
    5 dagar sedan

    Nice video

  72. Kouzoulos14
    5 dagar sedan

    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

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

      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.

    2. Kouzoulos14
      3 dagar sedan

      @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

    3. Vad3r
      3 dagar sedan

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

  73. Digota
    5 dagar sedan

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

  74. Orion Nash
    Orion Nash
    5 dagar sedan

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

  75. Greggy Dy
    Greggy Dy
    5 dagar sedan

    you lost me at “This one simple eQUaTioN”

  76. Lcx
    5 dagar sedan

    should i understand this video?! :)

  77. Jason Spades
    Jason Spades
    5 dagar sedan

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

  78. Camilo Delgado
    Camilo Delgado
    5 dagar sedan

    0:58 the video ended for me

  79. pravin rao
    pravin rao
    5 dagar sedan

    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

  80. pravin rao
    pravin rao
    5 dagar sedan

    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.

    1. pravin rao
      pravin rao
      5 dagar sedan

      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.

    2. pravin rao
      pravin rao
      5 dagar sedan

      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

  81. pravin rao
    pravin rao
    5 dagar sedan

    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

  82. Juseman
    5 dagar sedan

    If my girlfriend was an equation.

  83. Dreaming One
    Dreaming One
    5 dagar sedan

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

  84. Jose Medina
    Jose Medina
    5 dagar sedan

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    Error 10110
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    5 dagar sedan

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  87. FollowIfYouSwallow
    5 dagar sedan

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

  88. Stefan Papdi
    Stefan Papdi
    5 dagar sedan

    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

  89. Derek Da Luz
    Derek Da Luz
    5 dagar sedan

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

  90. Diego Mo
    Diego Mo
    5 dagar sedan

    Cool hyper dimensional Pringle you got there

  91. Dan iel
    Dan iel
    5 dagar sedan

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

    1. Dan iel
      Dan iel
      Dag sedan

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

    2. Segala Nicolas
      Segala Nicolas
      Dag sedan

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

  92. Ed Garzaro
    Ed Garzaro
    5 dagar sedan

    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.

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

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

  93. mario yu
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  94. Ismail Moufid
    Ismail Moufid
    5 dagar sedan

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

  95. Aayush
    5 dagar sedan

    Nyc Trick: 2:14

  96. Toon Vd Wielen
    Toon Vd Wielen
    5 dagar sedan

    Thanks man

  97. DevilCouldCare
    5 dagar sedan

    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).

    1. Segala Nicolas
      Segala Nicolas
      Dag sedan

      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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  99. Andrew Thomas
    Andrew Thomas
    6 dagar sedan

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

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