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

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År siden

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"

Karan Jassal
Karan Jassal Time siden
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 timer siden
hod up, someone has to tell me the graphing app that he used
Miagi Fodder
Miagi Fodder 3 timer siden
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 4 timer siden
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 4 timer siden
I don’t get any of this but it sounds awesome
Iron work Paul
Iron work Paul 5 timer siden
The content is very good, a wonderful man with interesting knowledge
Fuzzy Ankles
Fuzzy Ankles 6 timer siden
holy shiet thats beautiful
fffrikkie 123
fffrikkie 123 16 timer siden
Life is a simulation confirmed
Ishita Vyavahare
Ishita Vyavahare 19 timer siden
what software is he using?
Paolo Scaramuzzino
Paolo Scaramuzzino 20 timer siden
how does it apply to the Covid-19 waves?
O_0 21 time siden
Wait, so you're telling me that you could set equations on google's calculator this whole time? Amazing
Brian Kemery
Brian Kemery Dag siden
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 Dag siden
Anthony Tran
Anthony Tran Dag siden
first 10 seconds and i went dumb
Simon Lovelace
Simon Lovelace Dag siden
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 Dag siden
dolf1n1 Dag siden
Wow I love the way you presented this topic so visually.
Rocket Zing
Rocket Zing Dag siden
Veritasium : video ratio movie producer : ''m i joke to you
ash channan
ash channan Dag siden
how many leaves on a tree ? - search - NOpost Golden ratio Mrityunjaya Fibonacci Number Praveen Mohan - I like his explanation
Milkymalk Dag siden
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 Dag siden
Everything is under control of God. Everything, under His calculation. Assalamualaikum
XRay Plays
XRay Plays Dag siden
Phillip Plyer
Phillip Plyer Dag siden
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 Dag siden
I dont get it U just talk too much
Phineas 2 dager siden
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 2 dager siden
I just like the math... You'll die tomorrow, but the rabbits will forever live until.. Reality..
Mensa X
Mensa X 2 dager siden
All we have to do now is track and follow every bunny rabbit to see if this is true
rendzis 2 dager siden
In what day did god made this?😁
mazhar chrome
mazhar chrome 2 dager siden
Can you make a video about this equation with human population, where will be the equilibrium?
unityelt 2 dager siden
It's like programming life
Slow Motion
Slow Motion 2 dager siden
OMG! I bet he was the most hated guy in school !
Pula Vijaya
Pula Vijaya 2 dager siden
Is world an illusion make a video sir
Peacocks & Polar Bears
Peacocks & Polar Bears 2 dager siden
This is insane. I've never seen something visualized like this.
korteks visceralzen
korteks visceralzen 2 dager siden
Thanks. I love this channel. No one explains this stuff.
Betsy Larcom
Betsy Larcom 3 dager siden
I was an ecology major in undergrad and everyone else thought we just went around hugging trees...
Bare Bear Hands
Bare Bear Hands 3 dager siden
Chaos is natural order.
Eric Swenson
Eric Swenson 3 dager siden
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 3 dager siden
so random numbers are not so random.
Rohit Neemwal
Rohit Neemwal 3 dager siden
universal constants are just some values given to simulator to simulate our universe.hece we are in simulator
Rohit Neemwal
Rohit Neemwal 3 dager siden
so , we are in simulation .
Steven 3 dager siden
The mandelbrook fractal looks lika a turtle:)
Vinyas Singh
Vinyas Singh 3 dager siden
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 3 dager siden
You should make a podcast
O Templo de Shaka
O Templo de Shaka 3 dager siden
I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.
Hein Htet
Hein Htet 3 dager siden
There is no chaos. Everything has a pattern at certain perspective.
Martin Da Monarch
Martin Da Monarch 3 dager siden
That kinda looks like how a tree 🌳 grows lol cool
delt 4 dager siden
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
Ethan Evans 4 dager siden
Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago
CallMeBeep 4 dager siden
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kelvin Francisco 4 dager siden
This is the last time I watch any of your videos sober, 😒
Zee Y
Zee Y 4 dager siden
Now someone still thinks we live in a simulation?
Rohan Dongre
Rohan Dongre 4 dager siden
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 4 dager siden
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 4 dager siden
me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man
Pillow 4 dager siden
so this is how the multiverse go
Pillow 4 dager siden
Segala Nicolas
Segala Nicolas 4 dager siden
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 4 dager siden
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God 4 dager siden
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 4 dager siden
13:44 oh god it's the zodiac killer
Mugtba Moamed
Mugtba Moamed 4 dager siden
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 4 dager siden
How do you guys come up with such things.
Connor Eyer
Connor Eyer 4 dager siden
The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp
troeteimarsch 4 dager siden
mind blown and the day hasn't even started yet. thanks mate!
Chris Incorvati
Chris Incorvati 4 dager siden
Order begets chaos, chaos begets order.
Zygorg 4 dager siden
You adquired a new tittle: Chaotic (Neutral)
Carlos Handojo Santosa
Carlos Handojo Santosa 4 dager siden
You just blew my mind.
Holyfield Barrett
Holyfield Barrett 5 dager siden
The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason
GrandAdmiral Zod
GrandAdmiral Zod 5 dager siden
The anti-life/death equation?
ライアン 5 dager siden
rx - the population will grow exponentially rx - is a linear equation
Segala Nicolas
Segala Nicolas 4 dager siden
@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 4 dager siden
@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies
Релёкс84 4 dager siden
It is a linear *differential* equation, which translates to an exponential solution.
reckless bose
reckless bose 5 dager siden
The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter
Maeby Moore
Maeby Moore 5 dager siden
What happened to the contest after covid hit? Did the winner get to go?
Beulah West
Beulah West 5 dager siden
The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand
Brittany Baker
Brittany Baker 5 dager siden
The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year
RealJustinCase 5 dager siden
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
H o t r e t a r d e d c h i X 5 dager siden
Chaos is so subjective
Shoedi L
Shoedi L 5 dager siden
Overpopulation debukned.
Segala Nicolas
Segala Nicolas 4 dager siden
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 5 dager siden
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
Manuel Sánchez de Iñigo 5 dager siden
YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9
Scispace Facts
Scispace Facts 5 dager siden
Abdullah Bham
Abdullah Bham 5 dager siden
Design God
John Dalzell
John Dalzell 5 dager siden
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
tylor anderson 5 dager siden
When I say chaos, you say fogginbom, chaos
Mad Maniac
Mad Maniac 5 dager siden
I didnt understand anything
mark ryan Jervoso
mark ryan Jervoso 5 dager siden
When that needle happens on the chaotic part..then there will Thanos comes..
naysay02 6 dager siden
These numbers are living things. This is extraordinary.
Olli Bruno
Olli Bruno 6 dager siden
The real Question ist: how to apply this to the Stock market?
Kryptonicul 6 dager siden
Am i the only whos life is actually being changed by this stuff?? Its the only thing i can think about like all different types of infinity. Usually when im doing any task in my daily life ill spring into action or rather my brain does and starts think about how something can be infinite or is it infinite or can it be connected to infinity. The worst case of this is so simple but its almost hindering me, almost every two minutes in math class my brain just spits out "theres infinite amount of numbers in between ___ and ___" or "if you keep using that equation it will go for infinity" or even sometimes i try to make an infinite something like writing how many zeros after 0.0 before running out of room and having to put a 1 at the end. Tomorrow or maybe monday in class im going to use the mandelbrot equation to try and draw a small taste of a man made mandbrot set. Although I know I will be restricted by how much room I have on the page or whatever im drawing on. I almost feel restricted by reality or something. Considering everyone has ever told me that infinity is impossible to comprehend I seriously want to comprehend it or hear it or see it or just do anything that i could actually interact my sense with infinity. Of coure this will never happen considering there is no real infinity or at least not that we can "comprehend"
Manners PUBGM
Manners PUBGM 6 dager siden
The only reason we call it chaos is because in order to see the chaos as a constant you would need to be in a higher dimension.
Kim-André Johansen
Kim-André Johansen 4 dager siden
Yes! But maths can take us there 🙂
Leif Schmit-Kallas
Leif Schmit-Kallas 6 dager siden
The correct name for a population of rabbits is Fluffle.
Basil Al-jaml
Basil Al-jaml 6 dager siden
what is the name of the plotting tool at 3:07 ?
pudpud kirkpatrick
pudpud kirkpatrick 6 dager siden
The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield
Snow Ko Oo
Snow Ko Oo 6 dager siden
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😜
A Man With Suspenders
A Man With Suspenders 6 dager siden
4.669 hehehe funny number.
Jonas Fermefors
Jonas Fermefors 6 dager siden
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.
Enzhou Zutzut
Enzhou Zutzut 6 dager siden
This video makes me feel genius even though I don't understand any of it.
Axel From Group Therapy
Axel From Group Therapy 7 dager siden
Am i the only one who sees the graph similar to the Darwin´s tree of life?
Shark Falcon
Shark Falcon 7 dager siden
Amazing science communicator. Heads of to you sir!
Jack Barbey
Jack Barbey 7 dager siden
Wish I had seen this video when I was taking Dynamical Systems in college :/
O Riddle
O Riddle 7 dager siden
Bout to watch this fired af Hope it kick starts my physics degree
Brian Segovia
Brian Segovia 7 dager siden
The known doll preliminarily pat because buffer optimally carve between a unbecoming violet. likeable, wretched router
Marc030320 7 dager siden
So... we don't really need to worry about humans overpopulating the planet?
Segala Nicolas
Segala Nicolas 4 dager siden
In a sense, we don't : the population will reach and equilibrium, when the richest people will be able to afford the few resources that are left, and all the poor people will die. There will be less people, and the remaining people will be able to survive. But is that what we want ?
유유보현 7 dager siden
The fabulous lentil neatly shiver because hall empirically chew unto a sad pressure. maddening, tawdry population
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