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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
References:
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
archive.org/details/ShawRobertDrippingFaucetAsAModelChaoticSystem1984_201811/mode/2up
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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Jan 29, 2020

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Comments 100   
R Doody
R Doody 43 minutes ago
An application of math. Frustrating part of most math classes is the lack of application.
Leandro Placencia
Leandro Placencia 8 hours ago
19:39 10^10^100 Googolplex
Leandro Placencia
Leandro Placencia 8 hours ago
10^10^100 Googolplex
Rotciv Inoccic
Rotciv Inoccic 11 hours ago
BANG! .. My brain feels much better...
Netemp Witemp
Netemp Witemp 14 hours ago
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 20 hours ago
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
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
Holy hell. If they me a little about chaos theory in school I swear I would have been a mathematician by now.
ich
ich Day ago
Which software did he use for plotting his graphs? 3:45
Naz Fride
Naz Fride Day ago
Amazing. Thenks for the outstanding explanation of a pretty complex subject (for lay people)!
Subhadeep Das
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
Simranjeet Singh
Your calculation is wrong
Ssenyonjo Jireh
Can I still answer the question
Ssenyonjo Jireh
Can I still answer the question
Chindulur Sai Kaushik
out of all the possibilities z-axis was the least expected
Scripted Frames
we need "chaos" in schools, not the other chaos 😅
Scripted Frames
"Chaos"
Scripted Frames
This video proved me that I am a dumb
Scripted Frames
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 Day ago
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 Day ago
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
twobad Day ago
hod up, someone has to tell me the graphing app that he used
Miagi Fodder
Miagi Fodder Day ago
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 Day ago
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 Day ago
I don’t get any of this but it sounds awesome
Iron work Paul
Iron work Paul 2 days ago
The content is very good, a wonderful man with interesting knowledge
Fuzzy Ankles
Fuzzy Ankles 2 days ago
holy shiet thats beautiful
fffrikkie 123
fffrikkie 123 2 days ago
Life is a simulation confirmed
Ishita Vyavahare
Ishita Vyavahare 2 days ago
what software is he using?
Paolo Scaramuzzino
how does it apply to the Covid-19 waves?
O_0
O_0 2 days ago
Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing
Brian Kemery
Brian Kemery 2 days ago
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 2 days ago
ROWAN???
Anthony Tran
Anthony Tran 2 days ago
first 10 seconds and i went dumb
Simon Lovelace
Simon Lovelace 2 days ago
When the firing of Neurons in your brain and rabbits and Mandelbrot and Phi and oh my God it's everywhere
Juan David Barrada
Amazing!!!
dolf1n1
dolf1n1 3 days ago
Wow I love the way you presented this topic so visually.
Rocket Zing
Rocket Zing 3 days ago
Veritasium : video ratio movie producer : ''m i joke to you
ash channan
ash channan 3 days ago
how many leaves on a tree ? - search - USlift Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation
Milkymalk
Milkymalk 3 days ago
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 3 days ago
Everything is under control of God. Everything, under His calculation. Assalamualaikum
XRay Plays
XRay Plays 3 days ago
Huh
Phillip Plyer
Phillip Plyer 3 days ago
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
steve 3 days ago
I dont get it U just talk too much
Phineas
Phineas 3 days ago
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 3 days ago
I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..
Mensa X
Mensa X 4 days ago
All we have to do now is track and follow every bunny rabbit to see if this is true
rendzis
rendzis 4 days ago
In what day did god made this?😁
mazhar chrome
mazhar chrome 4 days ago
Can you make a video about this equation with human population, where will be the equilibrium?
unityelt
unityelt 4 days ago
It's like programming life
Slow Motion
Slow Motion 4 days ago
OMG! I bet he was the most hated guy in school !
Pula Vijaya
Pula Vijaya 4 days ago
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 4 days ago
I was an ecology major in undergrad and everyone else thought we just went around hugging trees...
Bare Bear Hands
Bare Bear Hands 4 days ago
Chaos is natural order.
Eric Swenson
Eric Swenson 5 days ago
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 5 days ago
so random numbers are not so random.
Rohit Neemwal
Rohit Neemwal 5 days ago
universal constants are just some values given to simulator to simulate our universe.hece we are in simulator
Rohit Neemwal
Rohit Neemwal 5 days ago
so , we are in simulation .
Steven
Steven 5 days ago
The mandelbrook fractal looks lika a turtle:)
Vinyas Singh
Vinyas Singh 5 days ago
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 5 days ago
You should make a podcast
O Templo de Shaka
I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.
Hein Htet
Hein Htet 5 days ago
There is no chaos. Everything has a pattern at certain perspective.
Martin Da Monarch
That kinda looks like how a tree 🌳 grows lol cool
delt
delt 5 days ago
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
Ethan Evans 5 days ago
Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago
CallMeBeep
CallMeBeep 5 days ago
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kelvin Francisco 5 days ago
This is the last time I watch any of your videos sober, 😒
Zee Y
Zee Y 6 days ago
Now someone still thinks we live in a simulation?
Rohan Dongre
Rohan Dongre 6 days ago
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 6 days ago
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 6 days ago
me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man
Pillow
Pillow 6 days ago
so this is how the multiverse go
Pillow
Pillow 5 days ago
multiverse
Segala Nicolas
Segala Nicolas 6 days ago
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
Michael 6 days ago
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God
God 6 days ago
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
Fractal 6 days ago
13:44 oh god it's the zodiac killer
Mugtba Moamed
Mugtba Moamed 6 days ago
Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.
Random X
Random X 6 days ago
How do you guys come up with such things.
Connor Eyer
Connor Eyer 6 days ago
The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp
troeteimarsch
troeteimarsch 6 days ago
mind blown and the day hasn't even started yet. thanks mate!
Chris Incorvati
Chris Incorvati 6 days ago
Order begets chaos, chaos begets order.
Zygorg
Zygorg 6 days ago
You adquired a new tittle: Chaotic (Neutral)
Carlos Handojo Santosa
You just blew my mind.
Holyfield Barrett
The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason
GrandAdmiral Zod
GrandAdmiral Zod 6 days ago
The anti-life/death equation?
ライアン
ライアン 6 days ago
rx - the population will grow exponentially rx - is a linear equation
Segala Nicolas
Segala Nicolas 6 days ago
@ライアン but it is exponential, because x(n+1)=r*x(n) is equivalent to x(n)=r^n so it's an exponential model because it's raised to a power. Anyway, the math here is correct
ライアン
ライアン 6 days ago
@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies
Релёкс84
Релёкс84 6 days ago
It is a linear *differential* equation, which translates to an exponential solution.
reckless bose
reckless bose 6 days ago
The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter
Maeby Moore
Maeby Moore 6 days ago
What happened to the contest after covid hit? Did the winner get to go?
Beulah West
Beulah West 6 days ago
The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand
Brittany Baker
Brittany Baker 6 days ago
The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year
RealJustinCase
RealJustinCase 6 days ago
I'm going to be so honest here. What the hell did I just watch and how do I feel even less about myself
H o t r e t a r d e d c h i X
Chaos is so subjective
Shoedi L
Shoedi L 7 days ago
Overpopulation debukned.
Segala Nicolas
Segala Nicolas 6 days ago
What do you mean ? That's not the point of the video, and I'm not sure what there is to debunk about overpopulation
USNBRENDON
USNBRENDON 7 days ago
CERN. August 1991. I believe it was few 6th.... But, yes, it was Switzerland's CERN that quietly switched on the first research website in the aim of studying particle based physics--atom smashing! Love it.
Manuel Sánchez de Iñigo
YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9
Scispace Facts
Scispace Facts 7 days ago
RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc
Abdullah Bham
Abdullah Bham 7 days ago
Design ..by God
John Dalzell
John Dalzell 7 days ago
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
tylor anderson 7 days ago
When I say chaos, you say fogginbom, chaos
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