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

2020-ж., 29-янв.
9 917 021 Көрүүлөр

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"

  • 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😜

    Snow Ko OoSnow Ko Oo3 саат мурун
  • 4.669 hehehe funny number.

    CerberusCerberus8 саат мурун
  • 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.

    Jonas FermeforsJonas Fermefors10 саат мурун
  • This video makes me feel genius even though I don't understand any of it.

    Enzhou ZutzutEnzhou Zutzut11 саат мурун
  • Am i the only one who sees the graph similar to the Darwin´s tree of life?

    Axel From Group TherapyAxel From Group Therapy16 саат мурун
  • Amazing science communicator. Heads of to you sir!

    Shark FalconShark Falcon17 саат мурун
  • Wish I had seen this video when I was taking Dynamical Systems in college :/

    Jack BarbeyJack Barbey17 саат мурун
  • Bout to watch this fired af Hope it kick starts my physics degree

    O RiddleO Riddle19 саат мурун
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    Brian SegoviaBrian Segovia20 саат мурун
  • So... we don't really need to worry about humans overpopulating the planet?

    Marc030320Marc03032021 саат мурун
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    유유보현유유보현Күн мурун
  • I gave up 1:35 in 🥲

    Emily uwuEmily uwuКүн мурун
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    Esther CookEsther CookКүн мурун
  • Nice video

    Tommaso D'EsteTommaso D'EsteКүн мурун
  • 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

    Kouzoulos14Kouzoulos14Күн мурун
  • So what you're saying is releasing an endemic pandemic wasn't worth it?

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

    Orion NashOrion NashКүн мурун
  • you lost me at “This one simple eQUaTioN”

    Greggy DyGreggy DyКүн мурун
  • should i understand this video?! :)

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

    Jason SpadesJason SpadesКүн мурун
  • 0:58 the video ended for me

    Camilo DelgadoCamilo DelgadoКүн мурун
  • 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 raopravin raoКүн мурун
  • 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 raopravin raoКүн мурун
    • 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 raopravin raoКүн мурун
    • 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 raopravin raoКүн мурун
  • 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

    pravin raopravin raoКүн мурун
  • If my girlfriend was an equation.

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

    Dreaming OneDreaming OneКүн мурун
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    Jose MedinaJose MedinaКүн мурун
  • Wut?

    Error 10110Error 10110Күн мурун
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    Jasper EcbJasper EcbКүн мурун
  • Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).

    FollowIfYouSwallowFollowIfYouSwallowКүн мурун
  • 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

    Stefan PapdiStefan PapdiКүн мурун
  • someone can tell me what is the program at minute 2:47? the program of graphs

    Derek Da LuzDerek Da LuzКүн мурун
  • Cool hyper dimensional Pringle you got there

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

    Dan ielDan ielКүн мурун
  • 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.

    Ed GarzaroEd Garzaro2 күн мурун
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  • i can assure you that not even half of the viewers understand enything 😂

    Ismail MoufidIsmail Moufid2 күн мурун
  • Nyc Trick: 2:14

    AayushAayush2 күн мурун
  • Thanks man

    Toon Vd WielenToon Vd Wielen2 күн мурун
  • 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).

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    Donnie BakerDonnie Baker2 күн мурун
  • Ok.....explain why when you multiply two negative get a positive number....? That one does my head in.

    Andrew ThomasAndrew Thomas2 күн мурун
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    Willy MadisonWilly Madison2 күн мурун
  • I watched this high and now I'm certain we live in a simulation.

    Flip MoreFlip More2 күн мурун
  • 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.

    Alberto HidalgoAlberto Hidalgo2 күн мурун
  • *y = mx + b has entered the chat*

    Beavalian _osuBeavalian _osu2 күн мурун
  • 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.

    Tom Georg EriksenTom Georg Eriksen2 күн мурун
  • i guess life really is entropy. time for another bong rip brb

    Samuel MasonSamuel Mason2 күн мурун
  • 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).

    NicolasNicolas2 күн мурун
  • Funny, the whole time I was watching this, I wonder why I never saw this in school

    James iPadJames iPad2 күн мурун
    • I think because this is a part of chaos. We student are not capable of handling chaos

      MakyrMakyr16 саат мурун
  • But how does it descend into chaos if the pattern happens every time at a specific value

    EvatanEvatan2 күн мурун
  • I stopped understanding when he started with the numbers... looks cool though

    Harryboi 64Harryboi 643 күн мурун
    • Same lol

      Kylie NelsonKylie Nelson2 күн мурун
  • I read about this in Nonlinear Dynamics

    AkileshAkilesh3 күн мурун
  • The answer to the question is CERN.

    Steven EatonSteven Eaton3 күн мурун
  • i. understand

    giagia3 күн мурун
  • This is what feels like after death

    Aditya KishoreAditya Kishore3 күн мурун

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

    Charge0CompleteCharge0Complete3 күн мурун
  • this guy is the madest scientist ever

    みみきP officialみみきP official3 күн мурун
  • i can`t stop thinking of epicnpcman`s fisherman.... (help)

    65 - Sebastian Fretes65 - Sebastian Fretes3 күн мурун
  • So many equations and models that repeat throughout life. Almost like it was programmed that way.

    A LA L3 күн мурун
  • 11:40 heartbeat pulse????

    Fernando MtlvoFernando Mtlvo4 күн мурун

    RobRob4 күн мурун
  • “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.

    MarkoMarko4 күн мурун
  • good video

    DomiNickelDomiNickel4 күн мурун
  • There should be a completely different field called the Mathematics of Nature. It's fascinating

    Nebuchadnezzar QuellcrisNebuchadnezzar Quellcris4 күн мурун
    • Mathematics itself is already nature. Why is this so hard for people to grasp? Is this forbidden knowledge? Lol

      NativeNative2 күн мурун
    • “Applied” usually implies that, For future reference.

      Pirkulator _Pirkulator _2 күн мурун
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    Jeremy DelgadoJeremy Delgado4 күн мурун
  • 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

    Zte PhoneZte Phone4 күн мурун
  • 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...

    Lavnish KumarLavnish Kumar4 күн мурун
  • I understand nothing 😥

    Govind Anand PathakGovind Anand Pathak4 күн мурун
  • We got graphs within graphs within graphs.

    Colm Óg GildernewColm Óg Gildernew4 күн мурун
  • can this equation be used to predict earthquakes?

    Damon Von BohnDamon Von Bohn4 күн мурун
  • apply this in music & cymatics and see what you get

    DarkSession van ArtDarkSession van Art4 күн мурун
  • 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

    Sammy MoktanSammy Moktan5 күн мурун
  • 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

    Sammy MoktanSammy Moktan5 күн мурун
  • Why are you using sounds and music to create emotions? That's not very fun ya

    Sammy MoktanSammy Moktan5 күн мурун
  • can this be applied to coronavirus?

    intarsia80intarsia805 күн мурун
  • genius! thank you!

    3263927 contra3263927 contra5 күн мурун
  • can i represent this equation with geogebra?

    Vitaly GrashchenkovVitaly Grashchenkov5 күн мурун
  • How relevant is the R number today... in a pandemic!!

    Abdullah Ali AkhtarAbdullah Ali Akhtar5 күн мурун
  • why did I rewatch this video feeling It has been 5 years since I've seen this

    Hemanth ReddyHemanth Reddy5 күн мурун
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    Kyra VijsmaKyra Vijsma5 күн мурун
  • cool vid, bro, but it kinda felt only like an appetizer

    Dr. GreenThumbsDr. GreenThumbs5 күн мурун
  • 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?

    GrizabeeblesGrizabeebles5 күн мурун
  • So pringles. Got it

    Lil WolfyLil Wolfy5 күн мурун
  • Me: sees the graph My brain: haha pp

    Caleb LarsonCaleb Larson5 күн мурун
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  • How did I get to 52 without hearing about it❗❓❗❓❗🚓🚔👮⚽

    Ramon IbarraRamon Ibarra5 күн мурун
  • why dont you use this to find the 0,6 of human population?

    KK5 күн мурун
  • The most "particularly active group of rabbits" would be at the Playboy mansion!

    unebonnevieunebonnevie5 күн мурун
  • Спасибо за субтитры

    Команда: ОтбитыеКоманда: Отбитые5 күн мурун
  • What did you use to graph the equation?

    Maxwell hm9040236Maxwell hm90402365 күн мурун
    • What software, I mean.

      Maxwell hm9040236Maxwell hm90402365 күн мурун
  • What graphing software is used?

    James HawkinsJames Hawkins6 күн мурун
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    thefunnymanthefunnyman6 күн мурун
  • Calls chaos gets constant... Hmmm...

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  • Minute 5 : Everything look distorted, I can see nothing but illusions and chaos. Too many bifurcations.. Now my mind bifurcated

    Bashar AhmedBashar Ahmed6 күн мурун