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

29 jan 2020
8 514 571 Áhorf

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"

  • Math is so freaking beautiful

    Aymee AlvarezAymee Alvarez7 klukkustundum síðan
  • I hope they teach like this in school

    Michael CabralMichael Cabral7 klukkustundum síðan
  • How are these graphics created?

    CJ SheppardCJ Sheppard14 klukkustundum síðan
  • It would be cool to have a glossary of key terms attached to each video

    CJ SheppardCJ Sheppard14 klukkustundum síðan
  • Well, most of that hurt my brain, but I think I get it. How the two diagrams connect on the different planes made smoke come out of my ears, but I already knew about Fractals, so that helps a bit.

    Ra PrometheusRa Prometheus15 klukkustundum síðan
  • Human growth rate is currently 1.05%

    CorrickCorrick15 klukkustundum síðan
  • sorry, can't understand this video... boring... at 10:40 i am leaving... bye !

    Adrian CiobotaruAdrian Ciobotaru16 klukkustundum síðan
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    Wallace KaedenWallace Kaeden17 klukkustundum síðan
  • - Can't explain long term outcome of 1 parameter equation in a way humans can understand - Deep learning algorithms with billions of parameters just need to have interpretable explanations to be trustworthy Good luck with that.

    Scott MillerScott Miller18 klukkustundum síðan
  • amazing vidoe

    Tristan_ SmithTristan_ SmithDegi Síðan síðan
  • respect ur explaination but it was a little too much complex

    Kirti SharmaKirti SharmaDegi Síðan síðan
  • Magnificent, i understand nothing

    Der AlteDer AlteDegi Síðan síðan
  • It didnt

    żorżżorżDegi Síðan síðan
  • really nice video , thank you !

    He MingdongHe MingdongDegi Síðan síðan
  • I quit physics when they Introduced time dilation to my life. Nerds.

    SAKET RoySAKET RoyDegi Síðan síðan
  • Just here to convince myself that I still love Physics and dont cram formulae.

    SAKET RoySAKET RoyDegi Síðan síðan
  • wait wait... Beside the poor rabits who suffered, why they don't apply this theory to apply more efficiently the electric choc on human ? it can save more lives ?

  • Hello, I have a question. Is the cellular division working this way ? Thanks !

    ratonlaveur79ratonlaveur792 dögum síðan
  • First step towards the salvation in this chaos is to know what a Feigenbum constant is!

    Vinayak SutarVinayak Sutar2 dögum síðan
  • Totally want a 3d sculpture of that now

    Evan LoydEvan Loyd2 dögum síðan
  • I had seen the bifurcation diagram before, but I never understood it until now. Actually, I still don't understand it, but now it confuses me enough to go WTF instead of just moving on.

    ganondorfchampinganondorfchampin2 dögum síðan
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    Nasser LOUIZNasser LOUIZ3 dögum síðan
  • he can make everything interesting.

    deepak turkardeepak turkar3 dögum síðan
  • this is the nurdiest thing ever

    وليد الخيروليد الخير3 dögum síðan
  • at some point the universe will hit the chaos and then stabilize again? is that what it is?

    Ramiez Ja'fariRamiez Ja'fari3 dögum síðan
  • isn't this similar to Covid spread calcs ? I recognized the "r" ...and not much else

    byronofcalgarybyronofcalgary3 dögum síðan
  • Best video ever. Brilliant. Thank you !

    peppermannpeppermann3 dögum síðan
  • I must have been cutting class. Anybody got a lighter?

    Mike BootAButtMike BootAButt3 dögum síðan
  • 9:50 what exactly are you plotting on the third axis? Is it the real component of the converged point at each c?

    Kyle BrownKyle Brown3 dögum síðan
    • I think it's the converged point, but only for real inputs of r.

      Lewis CarrollLewis Carroll14 klukkustundum síðan
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    FilhoDoCheateyFilhoDoCheatey3 dögum síðan
    • But, how about the down turn of the well equipped transient bladder twister that would never be caught playing the sharpest chords on the harp of the dunes of time. Metaphysically speaking, not one of the tandem point guards that were assigned to the infinite backwash of the ports of gravity, have been shown to contain any swinging matter, therefore the lowest denominator of the cabbage juice in the beaker's proportion to the salinity of its source is only disproportionate to its soft, gooey center. Bisons of North America!

      H ZH Z3 dögum síðan
  • I wish you got to how maps are used to study periodic behaviour of higher dimensional continuous PDEs (topic is "dynamical systems") But even after uni I never knew about the connection to the Mandelbrot set! Imma go do the maths to see why that happens

    Kyle BrownKyle Brown3 dögum síðan
  • what

    owa famosaowa famosa3 dögum síðan
  • You watch, it'll turn out the water drops individually will have the mandelbrot set inside of them as well.

    Brandon MooreBrandon Moore3 dögum síðan
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    daxter hunterdaxter hunter4 dögum síðan
  • If teachers taught this way and showed how exciting and interesting math can be, it could be life-changing for students who would otherwise be disinterested and end up failing

    Briana MBriana M4 dögum síðan
  • Is it reality is not chaotic, but simply mimicking chaos? xD

    Rômulo JallesRômulo Jalles4 dögum síðan
  • darpa

    Gene TowleGene Towle4 dögum síðan
  • 391K ppl pretending to have actually understood a single word he said

    mar comar co4 dögum síðan
    • @qwerty the way u wRite Mks u 1 Of M

      mar comar co2 dögum síðan
    • Well Not all of us r idiots. Only Some r.U d know.

      qwertyqwerty2 dögum síðan
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    P AlagaoP Alagao4 dögum síðan
  • I suppose it's not a coincidence that diagram looks like an evolutionary tree? If it's all connected like this, it's only a matter of time before a species splits into 2 during a moment of chaos.

    MadRazzMadRazz4 dögum síðan
  • Not all heroes wear capes. Thanks for this video man.

    Hugo ClarkeHugo Clarke4 dögum síðan
  • Learn something

    Vanessa BruceVanessa Bruce4 dögum síðan
  • Dear all, Does anyone know, which program he used around 3:30 to play with the function's parameters? Thank you!

    DerMatheAbiDerMatheAbi4 dögum síðan
  • wait wait hold on a second... where can i buy this 7:10 shadow light thingy?

    THE Riften GuardTHE Riften Guard4 dögum síðan
  • Poor rabbits.

    nonetheless qqqnonetheless qqq4 dögum síðan
  • Why these comment section is full of idiots

    sam kessam kes4 dögum síðan
  • The psychological ramifications of bifurcation: Homo erotic behavior is unexceptionable. Based on the endangerment of species propagation. X vs Y or X+Y? Is the question of survival.

    Larry BoothLarry Booth4 dögum síðan
  • It's clear that everything in the universe is orderly in some form or fashion. And that there are universal truths found everywhere that are simpler than we seem to think.

    James RussellJames Russell4 dögum síðan
  • Extremely complex this will take some time to get it

    Miguel GallardoMiguel Gallardo4 dögum síðan
  • This guy is smarted.

    Marco TontaMarco Tonta4 dögum síðan
  • The bouncy hardware connoly mess up because fiberglass literally wander astride a smelly detail. awful, chief respect

    Majed MarjiMajed Marji4 dögum síðan
  • This math is utterly fascinating! I never learned wasn't in school long enough really, which is a shame. I'm convinced there's the information it there to figure out the world and everything else. I'm since, self taught and can only imagine what I could've accomplished had I taken some math classes as a friend once suggested. I wish more kids today could understand how amazing everything is. Seems by the time you learn it, it never was really enough. Great view 👍👍

    Quick QuizQuick Quiz4 dögum síðan
  • I don't get it all from start to end but still click like and add to favorite hoping someday I will find this useful and will understand the topic.

    JebrozJebroz4 dögum síðan
  • Sorprendente , fabuloso. La naturaleza esconde muchos secretos que aun no descubrimos. Apasionante. Saludos

    Jorge CarrascoJorge Carrasco4 dögum síðan
  • The pretty hip naturally rot because distributor apparently annoy apropos a disagreeable dredger. aware, unarmed acknowledgment

    grade abstractgrade abstract5 dögum síðan
  • 4.6/2 = 2.3 I'm a 23rdian. I see it everywhere. is this a good thing or a bad thing, I really can't tell anymore lol

    W HW H5 dögum síðan
  • The unused objective inversely obtain because can positionally divide from a different flower. rightful, abstracted poultry

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  • Is this how Newton’s balls work? Graphed?

    Michael RogersMichael Rogers5 dögum síðan
  • Good show,

    Vigilance RiflesVigilance Rifles5 dögum síðan
  • There is no spoon.

    Justin McGuireJustin McGuire5 dögum síðan
  • poor rabbits

    a11312a113125 dögum síðan
  • If you were my teacher I would have loved math. Thanks for your videos

    ZachZach5 dögum síðan
  • Sad. You dont know how to read cause youre brainwashed lol. Still interesting.

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  • The bigger the poulation gets this year the *smaller* it will be next year? (circa 1 min 30 to 1min 38) Just take moment to think about that. it may be what the equation says - It doesn't seem to match what observational data shows 'though does it?

    FarweaselFarweasel5 dögum síðan
  • 13:42 man don't scientists have better things to do? Like they oughta be curing cancer or something.

    KasraKasra5 dögum síðan
  • We live in a simulation

    Chad mic macChad mic mac5 dögum síðan
  • 11 months 🤔 .. yes.”

    Malcolm AdamsMalcolm Adams5 dögum síðan
  • To bad people don’t, can’t, and won’t, understand what you are showing. This truth will die in you.. and by this time you should know why¿ but then again there’s no telling. 🤔 shh. Huh what you do with this information is where the real magic is. H u m a n.

    Malcolm AdamsMalcolm Adams5 dögum síðan
    • Ps the words^ this truth will die in you^ is not and in no way a declaration of war or inciting of riot. Case closed. Why must we protect the fragile ears of the populace. Maybe it is time to dig up that time capsule.

      Malcolm AdamsMalcolm Adams5 dögum síðan
  • Ok ( RC Christian ) I was born in 79’ & my brothers initials are RC. So, what I call it is.. Quantum looping. Now what’s the key 🔑:

    Malcolm AdamsMalcolm Adams5 dögum síðan
  • Change how I see the world? No, it didn't, but I did discover that this video makes a good alternative to sleeping pills.

    I Can Has KPopI Can Has KPop5 dögum síðan
  • I can remember reading that book by James Gleick in 6th grade. I heard him talk about it at the end and was like, "Oh my gosh, I remember that! That's so cool!"

    Michael FossMichael Foss5 dögum síðan
  • So, this equation will change how I see the world, How exactly? There is nothing in here that would make me change how I see the world

    BunkerFoxBunkerFox5 dögum síðan
  • Sir, this is a Wendy's 🍔

    Grafter HutchGrafter Hutch6 dögum síðan
  • i forgot the value of pi and started telling it out as 4.669

    47_Shreyas47_Shreyas6 dögum síðan
  • I’m a single dad of two boys and one girl. I was so skeptical at first as I have lost some money in crypto in the past and couldn’t even think of losing more as I didn’t have enough to take us. But when I started investing with bitvest24, I became happy again as I have made everything I lost and even more, I’m glad for such opportunity! Bitvest24 made my family happy again, keep up the good works!

    Samuel MuseSamuel Muse6 dögum síðan
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    esteban collazoesteban collazo6 dögum síðan
  • I bet it applies to government and learning too. I wonder if our lives use this in some way. Indeed the Universe/Multiverse may follow such a pattern.

    Matthew DanczMatthew Dancz6 dögum síðan
  • For anyone confused by this, it is because it was explained incorrectly. He is reading from a script between 0:49 and 1:17 and he defines the equation incorrectly. He says that X is the population of rabbits. That is not what X is. By the time you are two minutes in, he starts talking about it correctly. But it is REALLY clear that the narrator has limited knowledge of the topic. He also does not accurately explain the Mandelbrot set. This channel is bogus. Don't watch it.

    John GreenJohn Green6 dögum síðan
  • So then it wasnt actually CHAOS.. it was complex order... I like your videos alot... but you are misleading

    Blaq ShiepBlaq Shiep6 dögum síðan
    • chaos, at least how its defined, implies absence of order... True RNG... Which may or may not even exist in general... Surely, youre not going to tell me an science has cetegorically defined and ordered chaos, are you?

      Blaq ShiepBlaq Shiep6 dögum síðan
  • you lost me at "what"

    Jon DewarJon Dewar6 dögum síðan
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    4 KT4 KT6 dögum síðan
  • y’all didn’t bring up Nikola Tesla even once this was his life’s work

    TrueChoppaTrueChoppa6 dögum síðan
  • Veritasium: here’s a video of the bifurcation model. Me: ok. Sounds intriguing. (Click), let it rip. Veritasium: euddf353773eb265. 362gsbst2twjft3626agsgey3y2626fnfkg736{}/(,336{#:({)])]]). And then, if you simply 83heyey%4%;);), and then you 38374yeg,........ Me: 😳😳🤮🤮

    Steve LaPetersSteve LaPeters6 dögum síðan
  • "How did I get ot be 37 years old without hearing of the Feigenbbaum constant" -- my thoughts exactly. And there is a BS diploma in applied mathematics and physics collectng dust somewhere in my drawers. From a supposedly good univercity.

    Yuri BorzdyYuri Borzdy6 dögum síðan
  • Well, l am 13 years old, but i understand almost everything ( becouse of language barrier. i am from Russia) But it's just amazing! I've never seen anything like this! And even if i won't study it at uneversity i'm going to do it myself. Thank you for this video, it's very good

    Assasin Z3r0Assasin Z3r06 dögum síðan
  • "Simple equation"

    RouterRageRouterRage6 dögum síðan
  • i dont understand,,,,,

    CyberknightCyberknight6 dögum síðan
  • Lol, lab coats are retarded. They try to have metaphysics without God, which is impossible and retarded

    GetaidsGetaids6 dögum síðan
  • If this interests you but you don’t understand much of what he is saying, go to your nearest community college see what level math your at, and work towards Calc 3. You make it that far this dude will be making wayyyyyy more sense to you then. Holler at me if you need help filling out the application/ fasfa, or tutoring.

    Josh PingletonJosh Pingleton7 dögum síðan
  • And people say everything came out of nothing, nothing my asss. There is creator, A Master, Most Wise being, God! Everything created in a beautiful manner.

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  • So, lets figure out how far this will go with this youtube recommendation chain. I was impressed by the fact that seemingly there was 25k people who came from scythe lady video to the scythe festival one. From now on i am going to watch next 100 videos with this comment numerating my path. This is comment №48

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  • this is how I felt watching the third act of Interstellar

    Bella CurcioBella Curcio7 dögum síðan
  • I’ll just keep watching this video till it clicks

    GexGex7 dögum síðan