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 🙌
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. Abdullah Bham

    Abdullah Bham

    26 minuter sedan

    Design God

  2. John Dalzell

    John Dalzell

    55 minuter sedan

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

  3. tylor anderson

    tylor anderson

    Timme sedan

    When I say chaos, you say fogginbom, chaos

  4. Mad Maniac

    Mad Maniac

    2 timmar sedan

    I didnt understand anything

  5. mark ryan Jervoso

    mark ryan Jervoso

    2 timmar sedan

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

  6. naysay02


    5 timmar sedan

    These numbers are living things. This is extraordinary.

  7. Olli Bruno

    Olli Bruno

    5 timmar sedan

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

  8. Kryptonicul


    5 timmar 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"

  9. Manners PUBGM

    Manners PUBGM

    8 timmar 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.

  10. Leif Schmit-Kallas

    Leif Schmit-Kallas

    9 timmar sedan

    The correct name for a population of rabbits is Fluffle.

  11. Basil Al-jaml

    Basil Al-jaml

    13 timmar sedan

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

  12. pudpud kirkpatrick

    pudpud kirkpatrick

    14 timmar sedan

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  13. Snow Ko Oo

    Snow Ko Oo

    18 timmar 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😜

  14. Cerberus


    23 timmar sedan

    4.669 hehehe funny number.

  15. Jonas Fermefors

    Jonas Fermefors

    Dag 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.

  16. Enzhou Zutzut

    Enzhou Zutzut

    Dag sedan

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

  17. Axel From Group Therapy

    Axel From Group Therapy

    Dag sedan

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

  18. Shark Falcon

    Shark Falcon

    Dag sedan

    Amazing science communicator. Heads of to you sir!

  19. Jack Barbey

    Jack Barbey

    Dag sedan

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

  20. O Riddle

    O Riddle

    Dag sedan

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

  21. Brian Segovia

    Brian Segovia

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  22. Marc030320


    Dag sedan

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

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  24. Emily uwu

    Emily uwu

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    I gave up 1:35 in 🥲

  25. Hola Como Estas

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  27. Tommaso D'Este

    Tommaso D'Este

    2 dagar sedan

    Nice video

  28. Kouzoulos14


    2 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

    • Kouzoulos14


      9 timmar 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

    • Vad3r


      14 timmar sedan

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

  29. Digota


    2 dagar sedan

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

  30. Orion Nash

    Orion Nash

    2 dagar sedan

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

  31. Greggy Dy

    Greggy Dy

    2 dagar sedan

    you lost me at “This one simple eQUaTioN”

  32. Lcx


    2 dagar sedan

    should i understand this video?! :)

  33. Jason Spades

    Jason Spades

    2 dagar sedan

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

  34. Camilo Delgado

    Camilo Delgado

    2 dagar sedan

    0:58 the video ended for me

  35. pravin rao

    pravin rao

    2 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

  36. pravin rao

    pravin rao

    2 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.

    • pravin rao

      pravin rao

      2 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.

    • pravin rao

      pravin rao

      2 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

  37. pravin rao

    pravin rao

    2 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

  38. Juseman


    2 dagar sedan

    If my girlfriend was an equation.

  39. Dreaming One

    Dreaming One

    2 dagar sedan

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

  40. Jose Medina

    Jose Medina

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  41. Error 10110

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  42. Jasper Ecb

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  43. FollowIfYouSwallow


    2 dagar sedan

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

  44. Stefan Papdi

    Stefan Papdi

    2 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

  45. Derek Da Luz

    Derek Da Luz

    2 dagar sedan

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

  46. Diego Mo

    Diego Mo

    2 dagar sedan

    Cool hyper dimensional Pringle you got there

  47. Dan iel

    Dan iel

    2 dagar sedan

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

  48. Ed Garzaro

    Ed Garzaro

    2 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.

  49. mario yu

    mario yu

    2 dagar sedan

    The plucky cross hypothetically guess because mustard neuropathologically produce pace a many worm. sulky, awful tom-tom

  50. Ismail Moufid

    Ismail Moufid

    2 dagar sedan

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

  51. Aayush


    2 dagar sedan

    Nyc Trick: 2:14

  52. Toon Vd Wielen

    Toon Vd Wielen

    2 dagar sedan

    Thanks man

  53. DevilCouldCare


    2 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).

  54. Donnie Baker

    Donnie Baker

    2 dagar sedan

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  55. Andrew Thomas

    Andrew Thomas

    3 dagar sedan

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

  56. Willy Madison

    Willy Madison

    3 dagar sedan

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  57. Flip More

    Flip More

    3 dagar sedan

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

  58. Alberto Hidalgo

    Alberto Hidalgo

    3 dagar sedan

    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.

  59. Beavalian _osu

    Beavalian _osu

    3 dagar sedan

    *y = mx + b has entered the chat*

  60. Tom Georg Eriksen

    Tom Georg Eriksen

    3 dagar sedan

    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.

  61. Samuel Mason

    Samuel Mason

    3 dagar sedan

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

  62. Nicolas


    3 dagar sedan

    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).

  63. James iPad

    James iPad

    3 dagar sedan

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

    • Makyr


      Dag sedan

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

  64. Evatan


    3 dagar sedan

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

  65. Harryboi 64

    Harryboi 64

    3 dagar sedan

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

    • Kylie Nelson

      Kylie Nelson

      3 dagar sedan

      Same lol

  66. Akilesh


    3 dagar sedan

    I read about this in Nonlinear Dynamics

  67. Steven Eaton

    Steven Eaton

    3 dagar sedan

    The answer to the question is CERN.

  68. gia


    4 dagar sedan

    i. understand

  69. Aditya Kishore

    Aditya Kishore

    4 dagar sedan

    This is what feels like after death

  70. Oruga Margo

    Oruga Margo

    4 dagar sedan


  71. Elnora Winn

    Elnora Winn

    4 dagar sedan

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  72. Charge0Complete


    4 dagar sedan

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

  73. みみきP official

    みみきP official

    4 dagar sedan

    this guy is the madest scientist ever

  74. 65 - Sebastian Fretes

    65 - Sebastian Fretes

    4 dagar sedan

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

  75. A L

    A L

    4 dagar sedan

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

  76. Fernando Mtlvo

    Fernando Mtlvo

    4 dagar sedan

    11:40 heartbeat pulse????

  77. Rob


    4 dagar sedan


  78. Marko


    4 dagar sedan

    “Today'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. ” ― Nikola Tesla.

  79. DomiNickel


    4 dagar sedan

    good video

  80. Nebuchadnezzar Quellcris

    Nebuchadnezzar Quellcris

    4 dagar sedan

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

    • Native


      2 dagar sedan

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

    • Pirkulator _

      Pirkulator _

      3 dagar sedan

      “Applied” usually implies that, For future reference.

  81. Jeremy Delgado

    Jeremy Delgado

    4 dagar sedan

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  82. Zte Phone

    Zte Phone

    5 dagar sedan

    Look at Nassim Haramein's physics and his holofractalographic principle and you'll see that this can be applied on the universal scale as well as quantum scale

  83. Lavnish Kumar

    Lavnish Kumar

    5 dagar sedan

    My teacher in High School used to tell us that Every second thing in this Universe works on a mathematical pattern that is yet to be run down by us ... It all boils down to the fact that the people who actually worked on finding such patterns are the names that you may recall once the words Physics or Mathematics hits your mind (Say Einstein or Newton)... Nice Video Derek! ... The first time it really blew my mind but the second time, I was able to really relate it...

  84. Govind Anand Pathak

    Govind Anand Pathak

    5 dagar sedan

    I understand nothing 😥

  85. Colm Óg Gildernew

    Colm Óg Gildernew

    5 dagar sedan

    We got graphs within graphs within graphs.

  86. Damon Von Bohn

    Damon Von Bohn

    5 dagar sedan

    can this equation be used to predict earthquakes?

  87. DarkSession van Art

    DarkSession van Art

    5 dagar sedan

    apply this in music & cymatics and see what you get

  88. Sammy Moktan

    Sammy Moktan

    5 dagar sedan

    I'm at 14:34 now. You put a lot of effort. It's making me worked out. How is it that you're not famous of anything is what I'd like to say but dude you have a good idea about the thing you're doing

  89. Sammy Moktan

    Sammy Moktan

    5 dagar sedan

    Dude I'm at 17:39 you're really smart and are using good tricks but why do you not have a good fanbase? I could do something about it

  90. Sammy Moktan

    Sammy Moktan

    5 dagar sedan

    Why are you using sounds and music to create emotions? That's not very fun ya

  91. 3263927 contra

    3263927 contra

    5 dagar sedan

    genius! thank you!

  92. Vitaly Grashchenkov

    Vitaly Grashchenkov

    5 dagar sedan

    can i represent this equation with geogebra?

  93. Abdullah Ali Akhtar

    Abdullah Ali Akhtar

    5 dagar sedan

    How relevant is the R number today... in a pandemic!!

  94. Hemanth Reddy

    Hemanth Reddy

    5 dagar sedan

    why did I rewatch this video feeling It has been 5 years since I've seen this

  95. Kyra Vijsma

    Kyra Vijsma

    6 dagar sedan

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  96. Dr. GreenThumbs

    Dr. GreenThumbs

    6 dagar sedan

    cool vid, bro, but it kinda felt only like an appetizer

  97. Grizabeebles


    6 dagar sedan

    Here's a mad thought - the universe has gone through several different periods of expansion and quantum events are probabilistic. Could that related to chaos and the Feigenbaum constant?

  98. Lil Wolfy

    Lil Wolfy

    6 dagar sedan

    So pringles. Got it

  99. Caleb Larson

    Caleb Larson

    6 dagar sedan

    Me: sees the graph My brain: haha pp

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