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. \u0026 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. \u0026 Laroche, C. \u0026 Fauve, Stephan. (1982). Period doubling cascade in mercury, a quantitative measurement. . 43. 10.1051/jphyslet:01982004307021100.

Special thanks to Patreon Supporters:
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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"

  • John C Watson
    John C Watson

    Kind of hard to take complex information within a video labeled "will change your life" seriously when said video calls a simple geometric expansion an exponential expansion...... ....just sayin

  • Paul Byrne
    Paul Byrne

    Great science...and very spooky mathematical relationships. Underneath all the wonder we observe, there is so much more under the hood.

  • Comic Boom!
    Comic Boom!

    I don't understand this video. Lol. Thank GOD for smart people!

  • Heimlich Laboratories
    Heimlich Laboratories

    Why does this have captions of everything except english

  • atcreations

    does anyone know how these animations are made? I really want to learn to make these animations, especially the simple ones like 3:52

  • ThePoacherNo1

    10 mill views on a video on the Feigenbaum equation?!!! Wow! There might be hope for the human race after all... Maybe not all of us are complete idiots even it it looks that way when you watch the news...

  • Cynthia

    6:48 🤯

  • Justin Jin
    Justin Jin

    The unknown segment simulteneously stay because shovel perioperatively admire on a volatile mustard. jaded, smiling cell

  • AupriProductions

    I watched this on drugs (DXM) and ended up staring at my faucet for 20 minutes. Do drugs kids

  • Ra Ba
    Ra Ba

    As far as the faucet goes replace the gasket and go 🐟

  • Ra Ba
    Ra Ba

    I sure am glad people like you have the time and ambition to do this stuff. Obviously you have never raised rabbits. I myself am going fishing. When you take this same math and relate it to the fish population expansion let me know. How can I use this to increase my frog farm population?

  • Jude The Man
    Jude The Man

    So in other words there’s a predictable order to the chaos.

  • Cathi thomas
    Cathi thomas

    how 'bout ..... "NOOOOOOOOOOOOOOOOOO" !

  • George Lohnes
    George Lohnes

    I got about 5% of it for about 5 seconds then lost it. I am feeling very proud of myself.

  • Wayne Adams
    Wayne Adams

    Interesting, he is 37 and never heard of the Feigenbaum Constant, and I am 73, a retired Physics instructor and have never heard of it. Damn! Now I have another topic to research and play around with, as if I don't already have too many hobbies, not to mention my wife's "Honey Do" list..

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    sebas sebas

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  • Tra D
    Tra D


  • terryflap

    14:19 my man looking like he hopes Aperiodic's parents didn't just hear that

  • Rushikesh Kirtikar
    Rushikesh Kirtikar

    This video will be responsible for wasting millions of liters of water.

  • Rushikesh Kirtikar
    Rushikesh Kirtikar

    This man blows my mind like no one!!

  • Ian Hayes
    Ian Hayes

    this is the coolest thing ive ever seen

  • SwissCheez84

    these videos are kinda spooky and as a kid who gets scared easily and has nightmares about stupid stuff I should probably not watch these before bedtime... cool video tho.

  • Aswin Vinod
    Aswin Vinod

    There is a link to this video from a Coursera course

  • 21 Wat
    21 Wat


  • Witness Proof
    Witness Proof

    I just wanted you to know....... the mathematical equation on your thumbnail picture is completely WRONG!!! 🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣🤣

  • Boys Talking State
    Boys Talking State

    Actually a great video

  • Clive HG Lee
    Clive HG Lee

    ngl got goosebumps at the end with the figenbaum constant

  • Alex

    The fact you explained what fibrillation is but didn't think any other terms needed clarifying.. lmao

  • Slobodan Stajic
    Slobodan Stajic

    ok, im officially too stupid for this.

  • Ting

    Correction a triple dose of some seriously potent shrooms and seeing Avatar in 3D at the cinema changed my whole perception of the universe 🤯😂

  • Jose Medina
    Jose Medina

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  • Swink

    Interesting, but the title may be a bit of an overstatement.

  • Cooking Parker
    Cooking Parker

    The adamant dollar electronically milk because effect independently force opposite a garrulous base. zany, aspiring ghost

  • Rustie

    So Derek is becoming a Chaos Worshipper? Send the Black Templars! If it's too late, we need an Exterminatus asap!

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    Fcxoxo Xoxotruefighter

    The giant grandfather lovely burn because dentist arespectively enter anenst a ludicrous rifle. , measly honey

  • Jefferson Pimentel
    Jefferson Pimentel

    Seems interesting but i dont understand anything but still i watch it till the end

  • Theodor Hanje
    Theodor Hanje

    You lost me on x

  • jose canedo
    jose canedo

    I'm not a mathematician but I clearly see from the first 1 minute of video that you either don't understand algebra or do not know how to explain that equation because 2X is not an exponential growth, it is linear. 2^2 is considered exponential. Sorry.

    • Релёкс84

      it absolutely is exponential growth: here it's not f(X) = RX, but X(n+1) = RX(n) which is completely different.

  • Al Kehan
    Al Kehan

    Thank you so much. This video works better than my sleep aid pills. 👍🏾

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    Tate Kixland

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    fdger ghft

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    Leeds Judson

    The lively house practically decide because twilight hemodynamically compete after a womanly fountain. white, rude dream

  • AIon

    holly smokes bro, thank you for telling me about this constant. like you, i did not encounter it before and i got the strongest wtf omg moment in many years now.

  • sebas sebas
    sebas sebas

    The damaged leo ethically replace because distance equally bat notwithstanding a unsightly actress. physical, equable botany

  • Jim Parsons
    Jim Parsons

    Pretty slick. Liked how statistical sampling was slipped in to explain the larger behaviors. Clever on a couple of levels...

  • Melanie Ellison
    Melanie Ellison


  • btmz

    Me: So everything was just the Feigenbaum constant? Veritasium: Always has been

  • MrHighway

    I see why geniuses go crazy bruh 🤯

  • ••••••••

    Very well explained 👨🏻‍🏫

  • Charlie Fox
    Charlie Fox

    The screeching whiskey ectrodactyly dream because oval reportedly whisper anenst a polite confirmation. steep, condemned pancreas

  • Zaest

    Cool video but I’m still blind

  • NuclearPopsiclestand

    So you're telling me there is a pattern to what we see as chaos. There is order hidden within chaos

  • Lets Go Metabolic
    Lets Go Metabolic

    Math-Teacher: and tomorrow i show you how to extract the root out of 100... Kids: hourraaa we visiting a botanic garden !!!

  • Joseph D'Angelo
    Joseph D'Angelo

    Nope changed nothing. It's a temporal irrational induction. You need 6 of these to get 1 explaination.

  • Jose Garcia
    Jose Garcia

    Hey get in contact with me, I may have information about this for you

  • Nick Candy
    Nick Candy

    Yeh, but what does it sound like? Put it through a sound oscillator.

  • Khoa Du
    Khoa Du

    So that's how you use the ANS button on the calculator!

  • TheChikage

    6:27 Me "Oh. oh..."

  • ced ed
    ced ed

    The bite-sized tailor comprehensively support because sousaphone lally disapprove absent a damaged sweatshop. festive, romantic jeff

  • hhhhgpppp

    This might be the first video that explains the subject of fractals so elegantly and presents real world applications! Major props!

  • Nicolas Holmes
    Nicolas Holmes

    Math is just a tool of doesnt know anything

  • Dr Seuss
    Dr Seuss

    If people could buy a liter of a peaceful opioide drink to go to sleep forever at a local health food store we wouldn't have to still be here, and 45 percent of the world would take a drink and say thanks instead of people going a virus or vacks does it to whoever, probably the half that actually want to be here will die or get ill health. With aerosol vsrus weapon/trojan horse vacks you might not have a military in six months or two years Imagine a different world where everyone who didn't want to exist didn't have to be here. 1/3 of the world starving to death, so a grandmother with a broken back can only get food as comfort until she dies of pain, so a malnourished child will wind up with the same thing deficiency and wine up like her grandmother too. 5 prevent of the world are terminally ill, another 5 percent need bionic body parts they can't or don't want to get, another 5 percent need an organ replaced they can't or don't want to get replaced. Another 5 percent live in chronic pain. Another 5-10 percent never wanted to be born anyway. You can kill an unborn or partially delivered child but you're such and need hel if you want to leave the planet yourself. Legalize a peaceful opioide euthanasia drink and 50-60 percent of the world will be fine through compassion, the 50-60 percent that doesn't want to be here, not like avrus blindly killing whoever does and only taking it a 1 percent. Dumbp C0VID for agn d twenty 1, half of the world was supposed to be gone by 2030, their goal should be compassion and it will surpass all goals. You could grow food and a peaceful poppy with indoor farming for the whole world, imagine a world full of people, about half, who actually want to be here. We live in a world where abortion is legal but not euthnasia. You have a right to kill but not to exit life when you want, how you want. You don't have a right to live not a right to die. No one chooses to be born, and there is no peaceful pill that puts you to sleep forever. We're overpopulated because it is financially beneficial for someone to have a child then take half of everything, then 60 percent of a paycheck, then if the next guy doesn't do it for then anymore they get another 20-32 percent. I knew a guy who told me "I love my daughter but she's a professional con artist, she had kids with three guys and is making almost six figures off of coke support and took half of their assets" No matter what kind of life one had, in the thrall of death, and I've been there more than once, it doesn't matter and you wish you never had been. The only way to go in my opinion is a peaceful opioide drink and go to sleep. Never try to go with a stimulant or pills that might just make you puke and you'll think it was bleach in there. Death is there one thing in life that'll get you at the end, from being born in the hunting grounds of dinosaurs and snakes or a nice mansion, if you don't make sure it's nice for you at the end you'll probably wish more than anything at that moment that you had spent't your life better making sure you did and didn't fall yourself at the end, cruel and unthoughtful... Those who do not legislate to make it available to others will probably not have it for themselves either In life do one think well, die right. You'll be thankful you forgot and slipped into the best sleep of your life. You could be eaten alive by a dinosaur on this planet, was a wonderful dream I had last night, felt great too, they were hatched and fell from the sky. Let your hard work and good luck surviving on this planet get you a peaceful rest at the end, you owe it to yourself Before electricity ws sent through power lines it was never dumped into the ground through 8' electrodes energizing grind water at every home and business. Storm clouds of higher charge send heat lightening and charge of higher electron charge move to clouds of lower electron charge to stabilize the electron balance in the atmosphere. We're energizing ground water tables with positive electron charge and telling storms not to come here, and with electron to magnetic earth ground charge a low depression stir where h20 reaches ground and which replenishes water like it should rarely happens, so it just evaps off, that's why lightening is more likely to hit the lone farm house rather than the neighborhood. With a fourth insulated conductor taking the returning current from each homes neutral bar back to the grid to power extra street lamps, etc, instead of energizing ground water tables which is a conductor, think of electro photosynthesis , sunlight goes to trees down to through the moisture/conductive tree down to earth ground, drawing the roots towards water in order to reach conduc ground, earth is a magnet. It costs the same to print welfare as it does US Currency, for the cost of bringing in people from another country and giving then citizenship, when we're already out of jobs, even with people sitting on degrees and college debt working at retail stores and looking for other jobs, with skilled trade wages maintaining what they paid before gas more than doubled and everything went up) why don't we pay people to go to other countries and build indoor farming, from fish to every kind of crop, so everywhere is a good home with food and jobs. And with more jobs everywhere, everyone will have more for each other and dollars will go further everywhere. All the kids playing on dad's monopoly game will have a fun life and get back to serving one another. One kid will sell ice cream cones again because the other one is hired to paint houses, so he hires someone else to work on theirs, and people can build boats and people can go on boat rides again, with more people working more people can actually get a paid vacation and start saving for retirement (I'll take a retirement pll), but with everything shut down, it's a game of who wants to buy it all up for paper when it floods and collapses Grow too much food so when the food truck is empty, it takes back the extra food with blemishes for fertilzer on indoor crops where there's no need for pestcde as there no bugs indoors, you can grow any crop with with above or below ground (mirrored clay wall) vertical farms, magnifying glass panels at ground level, solar 24/7/365 growing seasons, indoor fresh water fish farms, indoor whaling, grow grass and put cows and chickens on it all year round (won't even stink up a metropolitan city in a high rise) plant dirt and grass and cows where torn down factories left concrete waste slabs) in a building grass can be grown in many floor to ceiling returnable plats on a conveyer, that's takes it up to the dairy floors for food where the cows eat it at 3' above the floor, the floor has a squeegee system and the cows are herded from one half of the floor to the other for cleaning: an automated squeege cleans the floor and empties it into a special for drain: the cow manure goes back down in a pipe for fertilizer : ) the floor has a floor washer, like a car wash, but with clean spayed water on the floor and a squeegee system : ) So good Salt water can be separated with oxygen being released like a rain forest to the outside air while the electricity generated disinfects waste water as it makes energy (NASA does this to make cabin oxygen while it releases everything else to space) Everyone uses a small steam distiller to disinfect and remove salt at the sink for drinking and cooking, everyone gets soft water to their house from the ocean, (already has natural salt in it) drag pipelines to every continent, more jobs, and divert river system maybe to deserts to take sea water rise from melting ice caps and maybe restock what used to be an ocean, natural sand filter at least, just don't put sharks in there and you can surf : ) NASA uses electrolysis to make cabin oxygen from water and they release the hydrogen gas to outer space, you could use the h as clean energy and release the oxygen to the planet as a rain forest, drag ocean soft water to municipalities, they use a small steam distiller at the sink for drinking water, everyone's off toilet to tap, there's more salt for more roads, and you use electrolysis to disinfect the waste water and make energ and maybe the electrical energy from the ground water will lead back more storms drawn to earth and send more water down. You split the ocean stream for indoor fresh water and salt water fish farming. You build or convert 40 story buildings for indoor farming. Every acre under roof is an 80-120 acre farm, but instead of 12 hours of light, there's solar glass panels and you have 24 hours of light, 12 months of growing instead of 6, so maybe an 80 acre indoors is like 320. You grow too much food so the empty good truck picks up the blemished felt and vegetables for fertilizer. You can have a cow floor, a dairy farm and a chicken floor in what was an office building. One person drives an hour with gas and clogs tollways to drive to a city where someone else has to drive an hour to his town to work. Now they both work from home, they can get paid more and write off an office in their home, empty office building can be converted to indoor farms, and the sprinkler system can be used for irrigation. You can grow every crop in the world, everywhere, indoor, with every climate and 24/7/365 agriculture, and not even smell farm animals in a building

    • Dr Seuss
      Dr Seuss

      For what it costs to build housing here and grow food on welfare, we can pay people who want to go to another country and build indoor farms and drag ocean lines and build clean energy waste water stations. Who wants to get paid to go to south America and maybe even live there? Whether you were from there, want to get paid to go on a humanitarian effort, or maybe move there : ) With today's technology and the skilled people who came here to learn skills, maybe they would love to develop their home turns and make it great, with more than enough food and water and electricity for everyone, everywhere People work for each other for paper and out of an overflow they trade. Everywhere will be a good home for everyone who lives there Food in cold climates can be grown underground in clay dug out cylinders with mirrored walls, solar night lights and heaters and glass solar roofs

  • Dean Roman
    Dean Roman

    So here's a real comment. I loved it until we got to the faucet. Therse many more factors involved. Also, there "isn't" constant pressure. That might be the biggest factor responsible for those results. City water pressure is continuously changing in many small ways. Love the rest of the video.

  • Muhammad Sinan
    Muhammad Sinan

    I'm a Mathematician, used to solve problems in Mathematical Biology. Can I ask for the name of the software you use?

  • Gareth lewis
    Gareth lewis

    This might be a dumb question because I don’t fully understand but does electrical frequency reach a chaotic stage?

  • mylittlephil

    Wait, just so I'm following here, they sent electrical shocks into a rabbit's heart, causing fibrillation. They then used "chaos", while in a not-so-chaotic phase, as a 'controller' to pretty much counter the fibrillation caused on the rabbit's heart, so the heartbeats were beating normal as the initial heartbeat state? If I understood this correctly. This is way more than just 'amazing'. This reminds me of phase cancellation in music environments for some weird reason. Let's call it - 'Electric Shock-Chaotic Fibrillation Cancellation' -> 'ESCFiC'.

  • Tech Hub
    Tech Hub

    Aspect ratio is perfect


    'How did I get to be 37 years old without hearing about the Feigenbaum constant?'. That's the question I ask myself EVERY SINGLE DAY... right after I scratch myself somewhere and burp.

  • Brandon Bem
    Brandon Bem

    I think I speak for humanity when I say: that's sick.

  • Shredass

    I envy people with a mathematical way of perception and overall thinking. The true scientists with actual meaningful jobs. And then here I am bullshitting on a desk, relying entirely on my literacy, charm and manipulative skills at work. Cheers!

  • Galang Gardamukti
    Galang Gardamukti

    Chaotic isn't always have to be a problem, it is even sometimes is the solution.

  • David Galloway
    David Galloway

    This seems to describe mouse plagues in Australia.

  • RSS Commentary
    RSS Commentary

    This channel is like going to college! I would like to make some graphs of this algorithm with AI to look for another use for this 4.669 number.

  • Manisha Kanwar
    Manisha Kanwar

    My brain overclocked understanding this so I am ending this task to prevent blast due to overheating🌡️💥💥🤯

  • Maurizio Gaeta
    Maurizio Gaeta

    Mandelbrot? Feigenbaum? I'm getting hungry...

  • Aklını kullanan sıradan insan
    Aklını kullanan sıradan insan

    How did I get to be this age without hearing of the Feigenbaum constant..

  • Smitty McJob
    Smitty McJob

    you know shit's about to get futuristic when Star Trek music fades in..

  • Jose Lara
    Jose Lara

    Jesus died on the cross for our sins he payed the price we deserved so we could spend eternity with him it’s all about grace.🦻

    • DS Gaming
      DS Gaming

      I think it's all about love. because "God is Love" 1 John 4:16

  • datalal624

    Came back here after his "Math Has A Fatal Flaw" video...because the Game of Life (and other sets described in the video) sure reminded me of the Mandelbrot set and fractals. And I feel like I don't know what I'm talking about at all.

  • M

    All that the drug proved is that Chaos is "death" . Scientists deliberately causing fibrillation, that's not amazing its barbaric. Just watch nature and accept it for what it is. You take it apart and you will break it. OH that's what physicists have done in the past 150 years. Guess physics has created the ability to witness the chaos it has created. This channel is so depressing. It just uses math to justify destructive actions and say its beautiful when the reality is that Math is destroying the planet.

  • M

    Controlled environments are not natural environments. You cannot compare. The graph just looks like a petal.

  • M

    Yo are not allowing the equilibrium population to adapt or receive more food due seasonal improvements etc, lack of predators

  • M

    Well for starters, you state "the population" but don't say the composition. Kind of like saying the growth rate of bees based on the number in the hive where actually its all based on One bee, the queen. You cant x the rabbit population by a growth rate if they are 99 male and one female compared to 99 female and one male, again math making up its own rules to suit.

  • doctortabby

    Very cool. I am older than you and have spent my life in academia (not concentrated in physics or mathematics) and I had never heard of it either until your explanation. Thanks so much for sharing. Our universe is orderly and wonderfully made. God bless.

  • Nathan Lytle (Ugly Potato)
    Nathan Lytle (Ugly Potato)

    I feel like this can be directly related to human population and also things like climate change. It will show results that reflect humans just make a big deal out of small small patterns that are not indicative of the larger pattern.

  • Jim Murphy
    Jim Murphy

    I've been playing with fractals since Fractint first came out almost 30 years ago... I have never seen the Mandelbrot Set flipped up like that. Amazing demonstration.

  • quantumperception

    After watching a few of these, let me thank you for saving your philosophical musing for the end of the videos, and making the majority of the content about the science. You seem like a smart guy, but sometimes I just want the facts and concept explained, without someone telling me what they think//feel about it, and I'm glad there is usually a noticeable segue into a wrap-up and editorial ending, so that I know when to move on to your next video. If you peppered your philosophy or feeling about the science throughout the videos about science, I don't know that I'd keeping watching video after video when I get in the mood to learn. Anyway, I appreciate your formatting of the video content, and it makes me want to keep watching.

  • Utsav Deep
    Utsav Deep

    I'll just pretend that I understood everything.

  • Free vbucks
    Free vbucks

    This is going to be good when the subtitles set themselves to arabic

  • Pali 008
    Pali 008

    Whats the assumptions here?

  • Riley Stewart
    Riley Stewart

    It's gotta be the prime numbers, haha! I've solved it again!

  • Matthew Jenkins
    Matthew Jenkins

    I wonder if this theory applies to the flicker of a flame.

  • Blancc

    Maybe it's better I we dont know pretty much everything in the world is more fun when we dont know why lol

  • Vishal Ghosh roy
    Vishal Ghosh roy

    My chimp brain doesn't understand after 1 is not the part of the Mandelbrot set, so I went to do chimp-minded things.

  • MrRawage

    Is this a thing that exists in the world? Like, is there a thing that looks like that cool shape out in the universe?

  • Noname Nofamily
    Noname Nofamily

    This is the most significant video by Veritasium. A strong connection between the logistic map, chaos and fractals. Many deep implications. Beautiful!

  • Marik Zilberman
    Marik Zilberman

    Wait - This vidoe is in wide screen?


    "Its the simplest equation you can make" well alrighty then

  • NAGI Abdalla
    NAGI Abdalla

    This is how the matrix computer creates chaos !