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

98 657 Shikime 10 mln

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. fffrikkie 123
    fffrikkie 123
    6 orë më parë

    Life is a simulation confirmed

  2. Ishita Vyavahare
    Ishita Vyavahare
    9 orë më parë

    what software is he using?

  3. Paolo Scaramuzzino
    Paolo Scaramuzzino
    10 orë më parë

    how does it apply to the Covid-19 waves?

  4. O_0
    11 orë më parë

    Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing

  5. Brian Kemery
    Brian Kemery
    15 orë më parë

    I've heard a ton about the Mandelbrot set over the years...but when he rotated it into 3 dimensions and it matched with the bifurcation diagram, my brain literally melted.

  6. KG Guitar
    KG Guitar
    15 orë më parë


  7. Anthony Tran
    Anthony Tran
    16 orë më parë

    first 10 seconds and i went dumb

  8. Simon Lovelace
    Simon Lovelace
    18 orë më parë

    When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere

  9. Juan David Barrada
    Juan David Barrada
    19 orë më parë


  10. dolf1n1
    Ditë më parë

    Wow I love the way you presented this topic so visually.

  11. Rocket Zing
    Rocket Zing
    Ditë më parë

    Veritasium : video ratio movie producer : ''m i joke to you

  12. ash channan
    ash channan
    Ditë më parë

    how many leaves on a tree ? - search - ALget Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation

  13. Milkymalk
    Ditë më parë

    What if all these fundamental constants are such weird numbers (4.669, 3.1415..., and so on) because the computer universe.exe runs on uses something other than base 10?

  14. adib z
    adib z
    Ditë më parë

    Everything is under control of God. Everything, under His calculation. Assalamualaikum

  15. XRay Plays
    XRay Plays
    Ditë më parë


  16. Phillip Plyer
    Phillip Plyer
    Ditë më parë

    I'm just now fi ding your videos and its creating chaos in my marriage! I feel a couple bifurcation coming on. Any sugar mommas out there wanna help me get to 4.6669!? 😜 But in all seriousness, your videos are awesome!

  17. steve
    Ditë më parë

    I dont get it U just talk too much

  18. Phineas
    Ditë më parë

    I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly

  19. John Worthington
    John Worthington
    Ditë më parë

    I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..

  20. Mensa X
    Mensa X
    Ditë më parë

    All we have to do now is track and follow every bunny rabbit to see if this is true

  21. rendzis
    2 ditë më parë

    In what day did god made this?😁

  22. mazhar chrome
    mazhar chrome
    2 ditë më parë

    Can you make a video about this equation with human population, where will be the equilibrium?

  23. unityelt
    2 ditë më parë

    It's like programming life

  24. Slow Motion
    Slow Motion
    2 ditë më parë

    OMG! I bet he was the most hated guy in school !

  25. Pula Vijaya
    Pula Vijaya
    2 ditë më parë

    Is world an illusion make a video sir

  26. Peacocks & Polar Bears
    Peacocks & Polar Bears
    2 ditë më parë

    This is insane. I've never seen something visualized like this.

  27. korteks visceralzen
    korteks visceralzen
    2 ditë më parë

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

  28. Betsy Larcom
    Betsy Larcom
    2 ditë më parë

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

  29. Bare Bear Hands
    Bare Bear Hands
    2 ditë më parë

    Chaos is natural order.

  30. Eric Swenson
    Eric Swenson
    2 ditë më parë

    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...

  31. Rohit Neemwal
    Rohit Neemwal
    3 ditë më parë

    so random numbers are not so random.

  32. Rohit Neemwal
    Rohit Neemwal
    3 ditë më parë

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

  33. Rohit Neemwal
    Rohit Neemwal
    3 ditë më parë

    so , we are in simulation .

  34. Steven
    3 ditë më parë

    The mandelbrook fractal looks lika a turtle:)

  35. Vinyas Singh
    Vinyas Singh
    3 ditë më parë

    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.

  36. Xer R
    Xer R
    3 ditë më parë

    You should make a podcast

  37. O Templo de Shaka
    O Templo de Shaka
    3 ditë më parë

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

  38. Hein Htet
    Hein Htet
    3 ditë më parë

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

  39. Martin Da Monarch
    Martin Da Monarch
    3 ditë më parë

    That kinda looks like how a tree 🌳 grows lol cool

  40. delt
    3 ditë më parë

    Seeeeriously fascinating!!!! 😲😲

  41. Ethan Evans
    Ethan Evans
    3 ditë më parë

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

  42. CallMeBeep
    3 ditë më parë

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

  43. Kelvin Francisco
    Kelvin Francisco
    3 ditë më parë

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

  44. Zee Y
    Zee Y
    3 ditë më parë

    Now someone still thinks we live in a simulation?

  45. Rohan Dongre
    Rohan Dongre
    4 ditë më parë

    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
      3 ditë më parë

      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.

  46. bereket taffesse
    bereket taffesse
    4 ditë më parë

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

  47. Pillow
    4 ditë më parë

    so this is how the multiverse go

    1. Pillow
      3 ditë më parë


    2. Segala Nicolas
      Segala Nicolas
      3 ditë më parë

      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

  48. Michael
    4 ditë më parë

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

  49. God
    4 ditë më parë

    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

  50. Fractal
    4 ditë më parë

    13:44 oh god it's the zodiac killer

  51. Mugtba Moamed
    Mugtba Moamed
    4 ditë më parë

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

  52. Random X
    Random X
    4 ditë më parë

    How do you guys come up with such things.

  53. Connor Eyer
    Connor Eyer
    4 ditë më parë

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

  54. troeteimarsch
    4 ditë më parë

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

  55. Chris Incorvati
    Chris Incorvati
    4 ditë më parë

    Order begets chaos, chaos begets order.

  56. Zygorg
    4 ditë më parë

    You adquired a new tittle: Chaotic (Neutral)

  57. Carlos Handojo Santosa
    Carlos Handojo Santosa
    4 ditë më parë

    You just blew my mind.

  58. Holyfield Barrett
    Holyfield Barrett
    4 ditë më parë

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

  59. GrandAdmiral Zod
    GrandAdmiral Zod
    4 ditë më parë

    The anti-life/death equation?

  60. ライアン
    4 ditë më parë

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

    1. Segala Nicolas
      Segala Nicolas
      3 ditë më parë

      @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
      4 ditë më parë

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

    3. Релёкс84
      4 ditë më parë

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

  61. reckless bose
    reckless bose
    4 ditë më parë

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

  62. Maeby Moore
    Maeby Moore
    4 ditë më parë

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

  63. Beulah West
    Beulah West
    4 ditë më parë

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

  64. Brittany Baker
    Brittany Baker
    4 ditë më parë

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

  65. RealJustinCase
    4 ditë më parë

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

  66. 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
    4 ditë më parë

    Chaos is so subjective

  67. Shoedi L
    Shoedi L
    4 ditë më parë

    Overpopulation debukned.

    1. Segala Nicolas
      Segala Nicolas
      3 ditë më parë

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

    4 ditë më parë

    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.

  69. Manuel Sánchez de Iñigo
    Manuel Sánchez de Iñigo
    4 ditë më parë

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

  70. Scispace Facts
    Scispace Facts
    5 ditë më parë


  71. Abdullah Bham
    Abdullah Bham
    5 ditë më parë

    Design God

  72. John Dalzell
    John Dalzell
    5 ditë më parë

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

  73. tylor anderson
    tylor anderson
    5 ditë më parë

    When I say chaos, you say fogginbom, chaos

  74. Mad Maniac
    Mad Maniac
    5 ditë më parë

    I didnt understand anything

  75. mark ryan Jervoso
    mark ryan Jervoso
    5 ditë më parë

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

  76. naysay02
    5 ditë më parë

    These numbers are living things. This is extraordinary.

  77. Olli Bruno
    Olli Bruno
    5 ditë më parë

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

  78. Kryptonicul
    5 ditë më parë

    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"

  79. Manners PUBGM
    Manners PUBGM
    5 ditë më parë

    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
      4 ditë më parë

      Yes! But maths can take us there 🙂

  80. Leif Schmit-Kallas
    Leif Schmit-Kallas
    5 ditë më parë

    The correct name for a population of rabbits is Fluffle.

  81. Basil Al-jaml
    Basil Al-jaml
    5 ditë më parë

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

  82. pudpud kirkpatrick
    pudpud kirkpatrick
    5 ditë më parë

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

  83. Snow Ko Oo
    Snow Ko Oo
    6 ditë më parë

    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😜

  84. A Man With Suspenders
    A Man With Suspenders
    6 ditë më parë

    4.669 hehehe funny number.

  85. Jonas Fermefors
    Jonas Fermefors
    6 ditë më parë

    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.

  86. Enzhou Zutzut
    Enzhou Zutzut
    6 ditë më parë

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

  87. Axel From Group Therapy
    Axel From Group Therapy
    6 ditë më parë

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

  88. Shark Falcon
    Shark Falcon
    6 ditë më parë

    Amazing science communicator. Heads of to you sir!

  89. Jack Barbey
    Jack Barbey
    6 ditë më parë

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

  90. O Riddle
    O Riddle
    6 ditë më parë

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

  91. Brian Segovia
    Brian Segovia
    6 ditë më parë

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

  92. Marc030320
    6 ditë më parë

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

    1. Segala Nicolas
      Segala Nicolas
      3 ditë më parë

      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 ?

  93. 유유보현
    7 ditë më parë

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

  94. Emily uwu
    Emily uwu
    7 ditë më parë

    I gave up 1:35 in 🥲

  95. Hola Como Estas
    Hola Como Estas
    7 ditë më parë

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

  96. Esther Cook
    Esther Cook
    7 ditë më parë

    The meek hardboard regrettably guarantee because anethesiologist ectrodactyly suffer next a protective walrus. medical, obscene toilet

  97. Tommaso D'Este
    Tommaso D'Este
    7 ditë më parë

    Nice video

  98. Kouzoulos14
    7 ditë më parë

    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
      3 ditë më parë

      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
      5 ditë më parë

      @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
      5 ditë më parë

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

  99. Digota
    7 ditë më parë

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

  100. Orion Nash
    Orion Nash
    7 ditë më parë

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