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

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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: www.fasthosts.co.uk/veritasium Code for interactives is available below...
Animations, coding, interactives in this video by Jonny Hyman 🙌
Try the code yourself: github.com/jonnyhyman/Chaos
James Gleick, Chaos
Steven Strogatz, Nonlinear Dynamics and Chaos
May, R. Simple mathematical models with very complicated dynamics. Nature 261, 459-467 (1976). doi.org/10.1038/261459a0
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). doi.org/10.1038/343653a0
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. dx.doi.org/10.1051/jphyslet:01982004307021100. 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:
epidemicsound.com "What We Discovered" "A Sound Foundation 1" "Seaweed" "Colored Spirals 4"
ve42.co/Artlist "Busy World" "Children of Mystery"

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29 gen 2020




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Commenti 100
Fairyplay 14 minuti fa
This video has become really relevant with covid lol (at least the R part at the beginning)
Ray Skudlark
I find it odd that ever since I can remember I have been trying to figure out this pattern 2 4 8 16 32 64 128 256 512 1024 as high as I could reach. And now to be learning all of this much later in life it really makes you wonder!? Thanks for the content man I have been watching and learning with you for I think what 8 or 9 years now and you have been a constant reminder I'm not the only one kicking these ideas around. I have been poor my whole life and never had a chance to apply my brain the way I wanted to. And being in low income areas it hard to have these kind of conversations with anyone. So thanks for doing this man really you and Micheal Vsauce I only hope the best to you guys.
C Harris
C Harris 3 ore fa
Finally the math that I already forgotten since high school looks interesting
Mathew Jackson
So I'm on the toilet, when you push more, more flow will come out but not all at once and evenly, then eventually your muscles can't take the stress and less flow will come out. Then your muscles recharge and you go at it again maybe harder or softer... Equation works in everything
Omid Khoshravan Azar
I don’t know why but this whole video felt like an unskippable ad
Maulau Craw
Maulau Craw 6 ore fa
Reverse this connection(selectablly applythe inverse function) and you have a fantastic modulus you can use to chart on an overlay the explicit proficiency to levels of implicit practicality of the teacher-student relevancy thereof.
bumfartbumfart2 10 ore fa
i hope you have won some awards for your films
The Zach
The Zach 14 ore fa
I think this graph also represents the evolution of human intelligence. 👉Think about this: The same brain that created the theory of evolution had to first evolve itself.
Mahir Balushi
Mahir Balushi 17 ore fa
Daniel Edwards
Daniel Edwards 17 ore fa
Brian Kleinschmidt
I love watching Mandelbrot renderings. That graphic just blew my mind. Beauty has a measure - math itself.
Lion Deluxe
Lion Deluxe 21 ora fa
This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.
mt2mgames 22 ore fa
this video is horrible. You keep conflating "the population" with "the percentage of the maximum possible population"
Marre Giorno fa
16:55 excited about chaos *HERESY* call the inquisiton
Ruderaksha Karwa
Showerthought: every civilization follows the same pattern , I would say we crossed the curve somewhere between 70s-90s
Drawing Masterclass
So much complexity and we still don't believe there is God.
Shawn Bechard
Shawn Bechard Giorno fa
I keep hearing predictions that human populations will decline, but I don't think it is going to be anywhere near as soon as they think. We have been rising since the Black Plague supposedly.
Nad G
Nad G Giorno fa
I LOVED this topic! It's insane! I knew that Mandelbrot set was pretty particular on its own but this! I want to know more
Ish Kabibble
Ish Kabibble Giorno fa
This is amazing! I'm familiar with the Mandelbrot set from decades ago, but is that 3D z-axis section a new discovery?
Look at me just 16 and finding out about this instead of 32 welp anyway I have to go troubleshoot my brain
Xandea Galleta
Xandea Galleta Giorno fa
I hurt myself in confusion. :(
Dodd Rougeau
Dodd Rougeau Giorno fa
Spherical trigonometry will prove the Earth is flat. You haven't got the balls to research that truth.
R Doody
R Doody Giorno fa
An application of math. Frustrating part of most math classes is the lack of application.
Leandro Placencia
Leandro Placencia 2 giorni fa
19:39 10^10^100 Googolplex
Leandro Placencia
Leandro Placencia 2 giorni fa
10^10^100 Googolplex
Rotciv Inoccic
Rotciv Inoccic 2 giorni fa
BANG! .. My brain feels much better...
Netemp Witemp
Netemp Witemp 2 giorni fa
It's the same about the human population. And it seems like we're at the peek right now and going down. That constant is like the pi of fractals
deck monkey
deck monkey 2 giorni fa
School only teaches you the minimum you need to start the next grade. It doesn't teach you to think or be intelligent and never will. Look at how fast kids learn until they start school and then are held back from learning at the same pace by being forced to do it "the way I tell you".
Jason Brunhard
Jason Brunhard 2 giorni fa
I want to thank you for your channel honestly. I rarely ever leave comments, but I am so IMPRESSED AND APPRECIATIVE for your work. You are bringing science out to the public forum so we, as a population, can engage in science. Science needs funding. It is what it is, and the content you provide is structured in a way for the general public can understand the unique and awe-inspiring physics that this universe has. FROM MY HEART THANK YOU FOR DOING YOUR BEST TO HELP THE HUMAN RACE EVOLVE.
The Rodestarr
The Rodestarr 2 giorni fa
Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.
ich 2 giorni fa
Which software did he use for plotting his graphs? 3:45
Naz Fride
Naz Fride 3 giorni fa
Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!
Subhadeep Das
Subhadeep Das 3 giorni fa
If everyone will become vegetarian, there is no hunting or poaching and no disasters then we can find the date of extinction of a specific species 😯😯😯😯😯😯. This is mind blowing
oh no
oh no 2 ore fa
this has nothing to do with vegetarians??
Simranjeet Singh
Simranjeet Singh 3 giorni fa
Your calculation is wrong
Ssenyonjo Jireh
Ssenyonjo Jireh 3 giorni fa
Can I still answer the question
Ssenyonjo Jireh
Ssenyonjo Jireh 3 giorni fa
Can I still answer the question
Chindulur Sai Kaushik
out of all the possibilities z-axis was the least expected
Scripted Frames
Scripted Frames 3 giorni fa
we need "chaos" in schools, not the other chaos 😅
Scripted Frames
Scripted Frames 3 giorni fa
Scripted Frames
Scripted Frames 3 giorni fa
This video proved me that I am a dumb
Scripted Frames
Scripted Frames 3 giorni fa
This video proved me that I am a dumb, I didn't even understand a bit as a 11th grades student
Leo Verran
Leo Verran 3 giorni fa
Rabbits times rabbits divided by coyotes plus hawks minus fox equals WTF are you talking about and who cares,...not even the rabbits care!
Karan Jassal
Karan Jassal 3 giorni fa
This video was so enlightening! Thank you! I love how we can visually see the fractal from a simple equation, and this is exactly how I perceive the universe. "As above, so below"
twobad 3 giorni fa
hod up, someone has to tell me the graphing app that he used
Miagi Fodder
Miagi Fodder 3 giorni fa
God man your 37 and only just found out about this. I'm 35 and just found out about it. Up your game dude
Xing Yu
Xing Yu 3 giorni fa
this vid has saved my essay project 😂i've been learning how to determine period doubling in the last couple of months. But i had little clue that so many real life phenomena exhibits the bifurcation doubling behaviour. Impressed!
FBI Agent
FBI Agent 3 giorni fa
I don’t get any of this but it sounds awesome
Iron work Paul
Iron work Paul 3 giorni fa
The content is very good, a wonderful man with interesting knowledge
Fuzzy Ankles
Fuzzy Ankles 3 giorni fa
holy shiet thats beautiful
fffrikkie 123
fffrikkie 123 4 giorni fa
Life is a simulation confirmed
Ishita Vyavahare
Ishita Vyavahare 4 giorni fa
what software is he using?
Paolo Scaramuzzino
Paolo Scaramuzzino 4 giorni fa
how does it apply to the Covid-19 waves?
O_0 4 giorni fa
Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing
Brian Kemery
Brian Kemery 4 giorni fa
I've heard a ton about the Mandelbrot set over the years...but when he rotated it into 3 dimensions and it matched with the bifurcation diagram, my brain literally melted.
KG Guitar
KG Guitar 4 giorni fa
Anthony Tran
Anthony Tran 4 giorni fa
first 10 seconds and i went dumb
Simon Lovelace
Simon Lovelace 4 giorni fa
When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere
Juan David Barrada
Juan David Barrada 4 giorni fa
dolf1n1 5 giorni fa
Wow I love the way you presented this topic so visually.
Rocket Zing
Rocket Zing 5 giorni fa
Veritasium : video ratio movie producer : ''m i joke to you
ash channan
ash channan 5 giorni fa
how many leaves on a tree ? - search - ITvid Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation
Milkymalk 5 giorni fa
What if all these fundamental constants are such weird numbers (4.669, 3.1415..., and so on) because the computer universe.exe runs on uses something other than base 10?
adib z
adib z 5 giorni fa
Everything is under control of God. Everything, under His calculation. Assalamualaikum
XRay Plays
XRay Plays 5 giorni fa
Phillip Plyer
Phillip Plyer 5 giorni fa
I'm just now fi ding your videos and its creating chaos in my marriage! I feel a couple bifurcation coming on. Any sugar mommas out there wanna help me get to 4.6669!? 😜 But in all seriousness, your videos are awesome!
steve 5 giorni fa
I dont get it U just talk too much
Phineas 5 giorni fa
I struggled to understand this just like many people. But look up Feigenbaum Number on Numberphile, it'll make this easier to understand slightly
John Worthington
John Worthington 5 giorni fa
I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..
Mensa X
Mensa X 5 giorni fa
All we have to do now is track and follow every bunny rabbit to see if this is true
rendzis 6 giorni fa
In what day did god made this?😁
mazhar chrome
mazhar chrome 6 giorni fa
Can you make a video about this equation with human population, where will be the equilibrium?
unityelt 6 giorni fa
It's like programming life
Slow Motion
Slow Motion 6 giorni fa
OMG! I bet he was the most hated guy in school !
Pula Vijaya
Pula Vijaya 6 giorni fa
Is world an illusion make a video sir
Peacocks & Polar Bears
This is insane. I've never seen something visualized like this.
korteks visceralzen
Thanks. I love this channel. No one explains this stuff.
Betsy Larcom
Betsy Larcom 6 giorni fa
I was an ecology major in undergrad and everyone else thought we just went around hugging trees...
Bare Bear Hands
Bare Bear Hands 6 giorni fa
Chaos is natural order.
Eric Swenson
Eric Swenson 6 giorni fa
And no one thinks there is a creator that did all this by design? All these links and ratios no one can explain the existence of, and we think it all just came about by accident...
Rohit Neemwal
Rohit Neemwal 7 giorni fa
so random numbers are not so random.
Rohit Neemwal
Rohit Neemwal 7 giorni fa
universal constants are just some values given to simulator to simulate our universe.hece we are in simulator
Rohit Neemwal
Rohit Neemwal 7 giorni fa
so , we are in simulation .
Steven 7 giorni fa
The mandelbrook fractal looks lika a turtle:)
Vinyas Singh
Vinyas Singh 7 giorni fa
I guess the made up/unexplained answer of "42" we get to hear about has something to do with this universal constant of "4.669", I'm not sure though.
Xer R
Xer R 7 giorni fa
You should make a podcast
O Templo de Shaka
O Templo de Shaka 7 giorni fa
I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.
Hein Htet
Hein Htet 7 giorni fa
There is no chaos. Everything has a pattern at certain perspective.
Martin Da Monarch
Martin Da Monarch 7 giorni fa
That kinda looks like how a tree 🌳 grows lol cool
delt 7 giorni fa
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
Ethan Evans 7 giorni fa
Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago
CallMeBeep 7 giorni fa
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kelvin Francisco 7 giorni fa
This is the last time I watch any of your videos sober, 😒
Zee Y
Zee Y 7 giorni fa
Now someone still thinks we live in a simulation?
Rohan Dongre
Rohan Dongre 8 giorni fa
What kind of math is that?? Initially you said X is no. of rabbits, then you choose X=0.4, how's that possible?? Now, if R is the rate of growth, population next year isn't X*R, but X*(1+R). Further if suggest that the rate of growth will depend on the present population, the R, for any year, will be expressed as a function of (Ps, Pp) where Ps is the saturation population assuming limited resources and Pp is the present population for that particular year. Therefore, Xn=RX(1-X) is incorrect.
Segala Nicolas
Segala Nicolas 7 giorni fa
The X is the percentage of population the theoretical maximum of the population. It makes sense to choose it arbitrarily, since what we care about is the value of X when it stabilises. And it will stabilise to the same value whether we choose it to be 0.4 or 0.9 or anything between 0 and 1. And secondly, it does make sense to multiply by the growth rate, as it makes an exponential model. The math here has been established since the 1970s, there are papers on this, of course it's correct.
bereket taffesse
bereket taffesse 8 giorni fa
me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man
Pillow 8 giorni fa
so this is how the multiverse go
Pillow 7 giorni fa
Segala Nicolas
Segala Nicolas 7 giorni fa
No, this has nothing to do with that. But if you want something that feels like the multiverse, you should check out Veritasium's video on the Many Worlds theory of physics
Michael 8 giorni fa
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God 8 giorni fa
THATS RIGHT!!! OH this got me so excited! :) Apply it to the cosmos and when a star releases energy to its surrounding planets. Chaos , adaptation to environment, then order but it evolves and branches out. The law of life. So many layers lol
Fractal 8 giorni fa
13:44 oh god it's the zodiac killer
Mugtba Moamed
Mugtba Moamed 8 giorni fa
Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.
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