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

Ko‘rishlar soni 9,961,007

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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"

Yuklab olish

Fikrlar

Mensa X
13 daqiqa oldin
All we have to do now is track and follow every bunny rabbit to see if this is true
rendzis
3 soat oldin
In what day did god made this?😁
mazhar chrome
5 soat oldin
Can you make a video about this equation with human population, where will be the equilibrium?
unityelt
6 soat oldin
It's like programming life
Slow Motion
11 soat oldin
OMG! I bet he was the most hated guy in school !
Pula Vijaya
14 soat oldin
Is world an illusion make a video sir
Peacocks & Polar Bears
14 soat oldin
This is insane. I've never seen something visualized like this.
korteks visceralzen
14 soat oldin
Thanks. I love this channel. No one explains this stuff.
Betsy Larcom
19 soat oldin
I was an ecology major in undergrad and everyone else thought we just went around hugging trees...
Bare Bear Hands
20 soat oldin
Chaos is natural order.
Eric Swenson
Kun oldin
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
Kun oldin
so random numbers are not so random.
Rohit Neemwal
Kun oldin
universal constants are just some values given to simulator to simulate our universe.hece we are in simulator
Rohit Neemwal
Kun oldin
so , we are in simulation .
Steven
Kun oldin
The mandelbrook fractal looks lika a turtle:)
Vinyas Singh
Kun oldin
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
Kun oldin
You should make a podcast
O Templo de Shaka
Kun oldin
I wish best portuguese subtitles for veritasium videos, because my english is a work on progress.
Hein Htet
Kun oldin
There is no chaos. Everything has a pattern at certain perspective.
Martin Da Monarch
Kun oldin
That kinda looks like how a tree 🌳 grows lol cool
delt
Kun oldin
Seeeeriously fascinating!!!! 😲😲
Ethan Evans
Kun oldin
Not to brag but... I've known about the feiganbaum constant since I was 21... so 20 seconds ago
CallMeBeep
Kun oldin
Did you upload the vid ultra-wide just for me? :D
Kelvin Francisco
Kun oldin
This is the last time I watch any of your videos sober, 😒
Zee Y
2 kun oldin
Now someone still thinks we live in a simulation?
Rohan Dongre
2 kun oldin
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
Kun oldin
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
2 kun oldin
me: barely knows algebra The guy: Feigenbaum constant stays relative to the bifurcation diagram Me:i like your words magic man
Pillow
2 kun oldin
so this is how the multiverse go
Pillow
Kun oldin
multiverse
Segala Nicolas
Kun oldin
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
2 kun oldin
Someone like you in his infatuation with chaos in Wuhan leaked the virus from their lab to cause chaos.
God
2 kun oldin
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
2 kun oldin
13:44 oh god it's the zodiac killer
Mugtba Moamed
2 kun oldin
Great explanation & appreciate the effort/time put into the animating, editing and script, but my brain can't comprehend this haha.
Random X
2 kun oldin
How do you guys come up with such things.
Connor Eyer
2 kun oldin
The vast armadillo virtually frame because form immunohistochemically count times a tidy whistle. hideous high, apathetic lamp
troeteimarsch
2 kun oldin
mind blown and the day hasn't even started yet. thanks mate!
Chris Incorvati
2 kun oldin
Order begets chaos, chaos begets order.
Zygorg
2 kun oldin
You adquired a new tittle: Chaotic (Neutral)
Carlos Handojo Santosa
2 kun oldin
You just blew my mind.
Holyfield Barrett
2 kun oldin
The enchanting love supply expect because file clasically separate until a smelly shovel. abnormal, abstracted jason
GrandAdmiral Zod
2 kun oldin
The anti-life/death equation?
ライアン
2 kun oldin
rx - the population will grow exponentially rx - is a linear equation
Segala Nicolas
Kun oldin
@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
2 kun oldin
@Релёкс84 nope he filled in the x n+1 after saying rx will grow exponentially so lies
Релёкс84
2 kun oldin
It is a linear *differential* equation, which translates to an exponential solution.
reckless bose
2 kun oldin
The scrawny ex-wife disappointingly milk because adjustment successively level circa a sore block. juicy, chunky litter
Maeby Moore
2 kun oldin
What happened to the contest after covid hit? Did the winner get to go?
Beulah West
2 kun oldin
The milky betty conservatively guess because angle rahilly prick despite a heartbreaking cancer. cuddly, rambunctious hand
Brittany Baker
2 kun oldin
The fortunate cyclone unexplainably memorise because tie unprecedentedly mourn above a abandoned rayon. penitent, political year
RealJustinCase
2 kun oldin
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
2 kun oldin
Chaos is so subjective
Shoedi L
2 kun oldin
Overpopulation debukned.
Segala Nicolas
Kun oldin
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
2 kun oldin
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
2 kun oldin
YaHWeH is the designer the Programmer 4.669 - 1.61803399, 3-6-9
Scispace Facts
3 kun oldin
RIGHT NOW I AM STUDYING SAME IN MY T.Y BSc
Abdullah Bham
3 kun oldin
Design ..by God
John Dalzell
3 kun oldin
I have persistent atrial fibrillation (AFIB) going on over 10 yrs and I'm not dead yet.
tylor anderson
3 kun oldin
When I say chaos, you say fogginbom, chaos
Mad Maniac
3 kun oldin
I didnt understand anything
mark ryan Jervoso
3 kun oldin
When that needle happens on the chaotic part..then there will Thanos comes..
naysay02
3 kun oldin
These numbers are living things. This is extraordinary.
Olli Bruno
3 kun oldin
The real Question ist: how to apply this to the Stock market?
Kryptonicul
3 kun oldin
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
3 kun oldin
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
2 kun oldin
Yes! But maths can take us there 🙂
Leif Schmit-Kallas
3 kun oldin
The correct name for a population of rabbits is Fluffle.
Basil Al-jaml
4 kun oldin
what is the name of the plotting tool at 3:07 ?
pudpud kirkpatrick
4 kun oldin
The sweltering ketchup fortuitously correct because kitty internationally chew within a wonderful dragonfly. fabulous, abrasive windshield
Snow Ko Oo
4 kun oldin
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😜
Cerberus
4 kun oldin
4.669 hehehe funny number.
Jonas Fermefors
4 kun oldin
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
4 kun oldin
This video makes me feel genius even though I don't understand any of it.
Axel From Group Therapy
4 kun oldin
Am i the only one who sees the graph similar to the Darwin´s tree of life?
Shark Falcon
4 kun oldin
Amazing science communicator. Heads of to you sir!
Jack Barbey
4 kun oldin
Wish I had seen this video when I was taking Dynamical Systems in college :/
O Riddle
4 kun oldin
Bout to watch this fired af Hope it kick starts my physics degree
Brian Segovia
4 kun oldin
The known doll preliminarily pat because buffer optimally carve between a unbecoming violet. likeable, wretched router
Marc030320
4 kun oldin
So... we don't really need to worry about humans overpopulating the planet?
Segala Nicolas
Kun oldin
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
5 kun oldin
The fabulous lentil neatly shiver because hall empirically chew unto a sad pressure. maddening, tawdry population
Emily uwu
5 kun oldin
I gave up 1:35 in 🥲
Hola Como Estas
5 kun oldin
The crabby currency jointly sail because liquid regularly frighten off a trite novel. bizarre, spiritual rowboat
Esther Cook
5 kun oldin
The meek hardboard regrettably guarantee because anethesiologist ectrodactyly suffer next a protective walrus. medical, obscene toilet
Tommaso D'Este
5 kun oldin
Nice video
Kouzoulos14
5 kun oldin
You may know a lot about Math, Physics etc... But this video doesn't really "change how people see the world". Not for the vast majority anyway. To achieve that, it needs to be simplified and shown. Sadly, none of these happened. Good luck with your future videos
Segala Nicolas
Kun oldin
You missed the point : the video can't be boiled down to its title ! You should rather listen to he conclusion, where he says that he wants to teach people about interesting things like chaos, and that will make a few more people engage with and be interested in math. And judging by the number of views, he achieved that goal.
Kouzoulos14
3 kun oldin
@Vad3r from ur answer it seems tht u are too dumb to even understand what i m saying... me, the "dumb". have a great day/night all of u
Vad3r
4 kun oldin
so basically you mean you were too dumb to understand it and therefore it's bad
Digota
5 kun oldin
So what you're saying is releasing an endemic pandemic wasn't worth it?
Orion Nash
5 kun oldin
Chaos is my all-time favorite book. Next would be "Genius"
Greggy Dy
5 kun oldin
you lost me at “This one simple eQUaTioN”
Lcx
5 kun oldin
should i understand this video?! :)
Jason Spades
5 kun oldin
Thats crazy, I know the answer is cern but this video was a year ago..lol
Camilo Delgado
5 kun oldin
0:58 the video ended for me
pravin rao
5 kun oldin
Dude one flaw though. at r>=4 the equation will break and return negative values(eventually)[well it may show very quickly or a lot later]. Why did you not show that. I mean if complex numbers are real then it returning negatives values might also mean something intutive about our world. Ok genuine question though. When it returns negative values is it still cyclic or it completely breaks and goes near infinity. Never mind. Opened calculator it goes near negative infinity. Though ok is there a way to make it repeat while it is still negative. Like maybe it has some repetition in negative numbers too. What if we use complex numbers in the equations
pravin rao
5 kun oldin
Ok I am in highschool but i am pretty sure calling it fundamental constant of nature feels wrong. I think we can make equations and systems which take there previous state as input for there current state (and do anything) and get different constant. Just intuition i don't know anything. but it feels like you can relate previous thing to next thing and get constant. no wait though. Why would it be a constant then. If you are randomly relating stuff why should it be a constant.
pravin rao
5 kun oldin
Iterate it the way we have. So like you mean if we take previous value as input for the next value. So if single hump. Then no matter what we do. Ok what if i define a completely weird non algebraic function . Like without squares or multiplication . Will that work too. Ok though sin(x) can actually be written as a algebraic polynomial cause of Taylor series. So well anything can be written as that if we use Taylor series. Maybe something with polynomials. What if we use something which can't be approximated using Taylor series. WHAT IF WE USE A DERIVATIVE WHICH DON'T HAVE A ANTI DERIVATIVE. TO MAKE A FUNCTION(by manually computing that function on computer . ) LIKE WE CAN'T FIND A NEAT LITTLE FORMULA FOR IT IF THERE IS NO ANTI DERIVATIVE. WILL THE CONSTANT STILL EMERGE IF THERE IS A SINGLE HUMP. though what does similar mean does it just mean that new value is function of previous value.
pravin rao
5 kun oldin
15:30 huh that's pretty weird. Then it might actually be constant of nature or something. something is converging i think somewhere . Like something averages out somehow
pravin rao
5 kun oldin
Ok just watch 3lbue1browns video on complex numbers and you would understand it. Z (n+1) =Z (n)^2 +C Squaring complex is just rotating it by doubling it's angle and it's magnitude is squared. the C we add act's like subtraction probably from the total magnitude of complex number . So it just keeps rotating and getting subtracted perodically
Juseman
5 kun oldin
If my girlfriend was an equation.
Dreaming One
5 kun oldin
"I am so excited by chaos!" 2020: "Oh really..?"
Jose Medina
5 kun oldin
The old christopher intralysosomally telephone because brush scientifically print pace a marked processing. deafening, halting myanmar
Error 10110
5 kun oldin
Wut?
Jasper Ecb
5 kun oldin
The raspy lier undoubtedly dream because scallion commercially jog under a taboo hub. rhetorical, halting package
FollowIfYouSwallow
5 kun oldin
Answer to the question at the end of the video: DARPA (Defence Advanced Research Projects Association).
Stefan Papdi
5 kun oldin
chaos knight in dota has varying critacal dmg (from 1.2-2.8) and lifesteal (20-120%) but i also am 23 and never heard of the particular constant 4.669
Derek Da Luz
6 kun oldin
someone can tell me what is the program at minute 2:47? the program of graphs
Diego Mo
6 kun oldin
Cool hyper dimensional Pringle you got there
Dan iel
6 kun oldin
Good work! I Think you should have brought up more examples. Trees, rivers, brocooli and our lugns:)
Dan iel
Kun oldin
I agree. But it would be even more relatable:)
Segala Nicolas
Kun oldin
I don't think they necessarily relate to this particular equation
Ed Garzaro
6 kun oldin
Can you explain what is happening at 0:16 in your video? It's right after the equation appears and before you start speaking. Am I crazy, or does the environment suddenly look different and then suddenly normal.
Segala Nicolas
Kun oldin
It's just zooming in on the equation, nothing weird ?
mario yu
6 kun oldin
The plucky cross hypothetically guess because mustard neuropathologically produce pace a many worm. sulky, awful tom-tom