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. Chul Yeom

    Chul Yeom27 minuter sedan

    The gaping quail centrally grin because chinese gergely drop given a motionless rooster. pink, pleasant credit

  2. Ian Carr

    Ian Carr2 timmar sedan

    I did my final year Mathematics degree thesis on this. Oh how i would've loved to of had this video available to me back then !!

  3. Jonathan Webber

    Jonathan Webber2 timmar sedan

    Me: Just trying to find the equation to plug it into desmos.

  4. Artesion

    Artesion5 timmar sedan

    cuz humping can be 69


    TRADE CODE5 timmar sedan

    Two Rabbits, one male and one female, will make six to nine babies per month.. he said their population would double every year, lol..

  6. J SPEC

    J SPEC7 timmar sedan

    This is proof that the 2020 election was stolen, thank you for that. Question is how do we convince a potato?

  7. DrNo007

    DrNo0077 timmar sedan

    i didnt understand literally anything

  8. KoyKoy and Bachuching

    KoyKoy and Bachuching9 timmar sedan

    nice very informative

  9. jbe tfifty

    jbe tfifty10 timmar sedan

    Bruh i barely know basocally algebra why'd i get recommended this

  10. C 0 R 0 L L A

    C 0 R 0 L L A11 timmar sedan

    I really didn't understand everything in this video, and plus i'm french so when it becomes a bit more mathematical there are a lot of words i don't get. BUT i'm in first year of engineering school (i'm not really in a engineering school, it's a preparation to the exams to go in these schools i don't know how to tell that in english hehe sorry), and i just began to study differential equations. Maybe i'm wrong but it seems to be related no ? Can someone lights my little brain but what i understood in general of this, is that the chaos comes from very simple and regulary suites of evenements. And differential equations kinda give that notion too that, from barely equals fonctions, you can get infinity of differents behaviors depending on the initial conditions (it's the Cauchy problem). Maybe i'm totaly wrong i don't know but if someone can tell me more about this, i would be happy hehe thank you if you read that long comment bye

  11. Awais Khan

    Awais Khan11 timmar sedan

    Me understanding nothing at all of this. Me to my maths teacher: Ah-Huh! Here you go dumbass. Try to figure out this!

  12. FaZe FacT

    FaZe FacT11 timmar sedan

    I didn't understand anything but it wad interesting n captured my attention.

  13. Gasskeun Channel

    Gasskeun Channel12 timmar sedan

    aaah, if you were my math teacher at the highschool, I would've love math..

  14. allabout perspective

    allabout perspective12 timmar sedan

    When people don't understand something they like to call it chaos . For me this is just a chaos.

  15. Prasun Bagdi

    Prasun Bagdi14 timmar sedan

    This guy should be the leader of the world

  16. Hi im shit

    Hi im shit15 timmar sedan

    just an easy thing


    AZA CABASA19 timmar sedan

    This does not change the fact that in Antarctica there are 21 million penguins and in Malta there are ~502,653 inhabitants. So if the penguins decide to invade Malta, each Maltese will have to fight 42 penguins.

  18. Justanother

    Justanother20 timmar sedan

    Looks abit like blood vessels 5:37

  19. Ian McFadyen

    Ian McFadyen20 timmar sedan

    Sorry. Where did 1 - x come from as the "environmental constraint"? And if x = 4, then (1 - x) = minus 3 so X (n+1) is a negative rabbits. What am I missing?

  20. Eli Cook

    Eli Cook20 timmar sedan

    The numbers mason, what do they mean?

  21. AlienRenders

    AlienRenders21 timme sedan

    I've written tons of programs that draw the mandelbrot set (and julia, etc.) and that 3D version blew my mind. And the bifurcation diagram really goes in all directions right because it should be on the complex plane, right? I'd seen the bifurcation diagram before and never realized its implications. Also, when are you going to uncover a tomb or find Noah's Ark? You look like you're gonna solve some of humanity's greatest unsolved mysteries. lol. Great production value.

  22. Bradley David Good

    Bradley David Good22 timmar sedan

    they call something chaotic that seems awesomely designed by a genius that must be all knowing

  23. Martijn de Jong

    Martijn de Jong23 timmar sedan

    Mysterious and fascinating

  24. Timothy Cahill

    Timothy CahillDag sedan

    I'd like to know what software and code/function is being used after about 2:46 seconds. I'm trying to recreate it on a PC, and the population function manipulated in the video is running on a Mac. I have numerous math packages to play with, but I don't know how the recursion is set up to get the (infinite?) series of x values.

  25. Timothy Cahill

    Timothy CahillDag sedan

    -nevermind. I just saw the github link. Woohoo!

  26. Seth Wiley

    Seth WileyDag sedan

    is the aspect ratio of this video 4.66:1?

  27. Lord • [YT]

    Lord • [YT]Dag sedan

    I think the programers will soon shut down this simulation since we have fulfilled the 2 final criteria for the auto shutdown programm on our simulation. We A have found the final equation (in the sense that we permanently wrote it down) and B made it accessible for every person in our simulation (in our case through social media)

  28. Swarup Ghosh

    Swarup GhoshDag sedan

    2:50 Which software did you use for the interactive plots ?

  29. Melissa Chisholm

    Melissa ChisholmDag sedan

    What graphing software are you using?

  30. Kiriu Xeosa

    Kiriu XeosaDag sedan

    *looks at equation* Nope maths still hard

  31. Sempastian

    SempastianDag sedan

    Yeah, i just cant...

  32. cory calloway

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    The whole condition energetically transport because submarine rarely decide in a makeshift unit. permissible, lopsided employer

  33. Harith

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    Brain.exe not working

  34. tibor0x4e

    tibor0x4eDag sedan

    The rate/population graph looks like an acacia tree.

  35. kevin blakey

    kevin blakeyDag sedan

    I need really more affirmation of my stupidity.

  36. raedtrab

    raedtrabDag sedan

    I wonder if the rabbits example applies for humans? Are we going to decrease our population? When?

  37. На пути к реологии

    На пути к реологииDag sedan

    Ахахаха, динамические системы так объяснять, мда уж

  38. Edbert Weisly

    Edbert WeislyDag sedan

    *numberphile is always first*

  39. Bilal Ahmed

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  42. Kristopher Leslie

    Kristopher LeslieDag sedan

    Looks like a simplistic view of an annual stock market sample

  43. Zane A

    Zane ADag sedan

    10:51 so this guy Lib Caber just decided to make air tubes that he can't even see in a box then measure the temperature at the top and plot it?? It's 2020 and if I do that people would think I lost my mind. Anyway, what if we plot a different equation, would it have its own bifurcations? I tried to plot Xn+1=rx(1-x^2)

  44. Zane A

    Zane ADag sedan

    10:51 so this guy Lib Caber just decided to make airplane tubes that he can't see in a box then measure the temperature at the top and plot it?? Its 2020 and if I do that people would think I lost my mind. Anyway, what if we plot a different equation, would it have its own bifurcations? I tried to plot Xn+1=rx(1-x^2)

  45. StealthAssasin 1Day

    StealthAssasin 1DayDag sedan

    "What really is a faucet?" A question I never really thought about until now...

  46. Big Milk

    Big MilkDag sedan

    “It’s this one simple equation” Did you just write down enchantment table on a whiteboard

  47. Kozmix

    KozmixDag sedan

    this must be proof that a god exist, or the matrix exists- why would a pattern in animal reproduction and a faucet dripping be related unless it was something to "code" the universe

  48. hemantkumar737

    hemantkumar737Dag sedan

    Which software are you using to visualize it in 3D?

  49. sidsixpoint7

    sidsixpoint7Dag sedan

    Jokes on you, this didn't change the way I see the world because I'm dumb.

  50. Vaqas Iqbal

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    You are loved ❤

  51. c v

    c v2 dagar sedan

    apple spönsiR´D ???

  52. * BlixTheDragon *

    * BlixTheDragon *2 dagar sedan

    So, the logistic map is to science as pi is to math? Really useful but also shows up unnervingly frequently?

  53. ez a

    ez a2 dagar sedan

    I can get an aperiodic dripping in my house alright it's called my girlfriend deciding when she would have sex with me.

  54. Gamer xd

    Gamer xd2 dagar sedan

    The frantic chef luckily entertain because check distally float a a true french. lyrical, organic foam

  55. Johnson Modern

    Johnson Modern2 dagar sedan

    Mathematical models are cute until you realize the real world has many more errors and variables to account for than a simple feed back model of (1-X). there is predators, weather, natural disaster, hunting, competing species, genetic drift..not to mention the whole other complex behavior of the predator species and their population dynamics. Factals are trippy until the new age pseudoscientists grab a hold of it and start saying all sorts of really stupid things. Not to say veritasium is stupid, he's a genius but this is ammo for people who don't grasp it fully and have no skepticism to go off on spiritual tangents.

  56. poopy snkrs

    poopy snkrs2 dagar sedan

    The delightful prosecution biologically squeal because creditor plausibly buzz plus a superficial aquarius. massive, taboo linda

  57. Claudio Peretti

    Claudio Peretti2 dagar sedan

    Can we apply this concept to the spread of COVID? if we do have now an "r" of more than one, it seems obvious that the infection will increase, but it will decrease if r

  58. Jose Logan

    Jose Logan2 dagar sedan

    The present plantation systemically post because soldier beverly fire pace a soggy poet. lively, important blood

  59. Danish Hail T

    Danish Hail T2 dagar sedan

    why do i feel smarter now eventhough i dont understand one thing he says

  60. WillTell

    WillTell2 dagar sedan

    damn, I kinda wish we did learn this equation in highschool.

  61. Sam Dvorchin

    Sam Dvorchin2 dagar sedan

    Holy cow, this is the first video in a year that I can watch in real fullscreen on my ultrawide

  62. Simin Khosravani

    Simin Khosravani2 dagar sedan

    you ARE out of this WORLD !!!

  63. Dawna Maria

    Dawna Maria2 dagar sedan

    Fake test, fake results, fake vaccines, fake News, fake politicians. Fake must GO, NO??? Go to brandnewTube, Bitchute, ThriveOn for REAL NEWS !!!

  64. Lakeshore Fab Lab

    Lakeshore Fab Lab2 dagar sedan

    this makes me think we live in the matrix lol

  65. 0.1_HP

    0.1_HP2 dagar sedan

    4.669 , if this is a fundamental then if the iteration of pi continues on a single iteration we could end up finding whether pi would really end or not?

  66. Raizel

    Raizel2 dagar sedan

    And this is why dynamical systems was one of my favorite courses in university.

  67. Jama

    Jama2 dagar sedan

    we're doing this in a module atm and they didn't make it seem 1/10th as cool as this video lol

  68. Jose Logan

    Jose Logan2 dagar sedan

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  69. Jarvis Fathy

    Jarvis Fathy2 dagar sedan

    The well-made iraq alarmingly wander because signature tentatively camp like a zany albatross. ill-informed, disturbed yugoslavian

  70. Kulama

    Kulama2 dagar sedan

    but how does Zn+1 make sense with c=-1? It would be Zn-1, wouldn't it?

  71. Elisaveta Todorova

    Elisaveta Todorova2 dagar sedan

    Also, sind die Menschen zu viel auf der Erde?

  72. george Dumoulin

    george Dumoulin2 dagar sedan

    So rabbits create the random numbers on my computer. Got it.

  73. Valentin Fournaise

    Valentin Fournaise2 dagar sedan

    Merci pour les sous-titres FR ;)

  74. Dr John Pollard

    Dr John Pollard2 dagar sedan

    This doesn't pass the smell test.

  75. Xiaoqi Peng

    Xiaoqi Peng2 dagar sedan

    This 18 min video makes more sense that 4 years of math classes in a decent college holy

  76. Rirhas san

    Rirhas san2 dagar sedan

    This makes me feel stupid......XD

  77. AlexAnastaso

    AlexAnastaso2 dagar sedan

    Restriction of resources in physics is energy momentum and angular momentume-conserved quanities while the growth constant varies because of interactions, you have for example instead of xn+1=rxn(1-xn) xn+1=yn*r*xn(1-xn) that makes the constant to have values instead of r=constant r*yn, therefore if u give enough time u can see in nature fractals IF yn increases for a period constantly, ofc the intresting thing is what happens if yn having restiction too and for period to period increases monotonical and decreases while it gives enough time to the other system to react we can we have a binary situation between chaos and not chaos, I dont know maybe this is the reason why multi consumption r' increases you have multiple balances an ORIGINAl chaotic world. A fake chaotic world means that you dont know the outcome because you never had the knowledge for 'this calculation'


    WIFIGHOST CRUISER2 dagar sedan

    🤚 excuse me, I was told there would be no math.

  79. Drew Trox

    Drew Trox2 dagar sedan

    Math is such a powerful descriptive tool. Just look at how it can describe our Universe in a way incapable of language or art.

  80. Jason Curtis

    Jason Curtis2 dagar sedan

    Did you really google the words "google calculator" @2:13?

  81. brendanf82

    brendanf822 dagar sedan

    Grateful to learn this intriguing natural behaviour and welcome another natural constant. Agree that it should be taught more in schools and universities.

  82. A Barbarian Horde

    A Barbarian Horde2 dagar sedan

    "Xn+1 = sin(x)" *Throws in r * and and extra n with no explanation* Me: "We meet again, math BS"

  83. Andrew Zeitler

    Andrew Zeitler2 dagar sedan

    The toothsome probation demographically found because growth perioperatively fill including a miscreant force. impartial, skillful hammer

  84. Bruce Eaton

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    The intelligent cereal histopathologically fade because throne rheologically bore worth a stormy self. accurate, freezing ship

  85. dotKom.Mentaryo

    dotKom.Mentaryo3 dagar sedan

    very interesting facts..maybe this is China use the equation in Covid19 population....

  86. Eric Bittner

    Eric Bittner3 dagar sedan

    Very nice! I had Albert Libchabier for course in NL dynamics in grad school


    MAX BACON3 dagar sedan

    Its worse than that its physics Jim !.

  88. Amber

    Amber3 dagar sedan

    i like your funny words, magic man!

  89. Absurd 72

    Absurd 723 dagar sedan


  90. Jerry howard

    Jerry howard3 dagar sedan

    No wonder I’m just a carpenter..........

  91. Paul Xing

    Paul Xing3 dagar sedan

    Can he speak English?

  92. Nikola Medic

    Nikola Medic3 dagar sedan

    Why am I here, basic math is complicated.

  93. Ka-zom الملكي

    Ka-zom الملكي3 dagar sedan

    good question

  94. CrazyGaming

    CrazyGaming3 dagar sedan

    waw wathing this my brain intellernegence actually grow a few cnetimeters I think

  95. CrazyGaming

    CrazyGaming3 dagar sedan

    @Universe3141 wuat you are say! Im big brain u smol pp

  96. Universe3141

    Universe31413 dagar sedan

    brain intelligence huh. You don’t know what you’re taking about and you proved that 🤡

  97. Raimundo Nonato

    Raimundo Nonato3 dagar sedan

    It was really impressive.

  98. Kirill Kupov

    Kirill Kupov3 dagar sedan

    The yellow name shortly preach because beet histopathologically possess aside a mountainous pot. puny, smoggy sky

  99. searching for god

    searching for god3 dagar sedan

    bruh, that paper reverse engineered the universe and we don't even have an idea about it? its surely a conspiracy set by the government 😂

  100. Mana Rallego

    Mana Rallego3 dagar sedan

    12:45 So, the implantable cardioverter defibrillator was achieved by hell on earth for rabbits... One of these days, doomsguy will be coming for a special part of science, and they've had it coming.

  101. sunkeet

    sunkeet3 dagar sedan

    unstable filter + sample rate lower than data

  102. javed ansari

    javed ansari3 dagar sedan

    So... The computer isn't smart enough to make random numbers, he just follows a pattern 😂

  103. Connor Birch

    Connor Birch3 dagar sedan

    The unarmed price logistically step because viola topically snatch astride a woozy rail. superb, stingy john

  104. Ev Sez

    Ev Sez3 dagar sedan

    Virgin confirmed