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. 01. 2020





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Komentáře 100
Whois Slimshady
Whois Slimshady Před hodinou
Andrew Post
Andrew Post Před 2 hodinami
"One leads to two, two leads to three, three leads to all things..." (Tao Te Ching)
Hakimuddin Diwan
Hakimuddin Diwan Před 3 hodinami
Warning: Watching this video for more than 5 minutes will cause instant intensive regreat.
Dedek Arda
Dedek Arda Před 3 hodinami
my brain has stopped working
beyackabiotch Před 5 hodinami
SXSW!!! OMG what a long excruciating year that was
hitesh bonde
hitesh bonde Před 12 hodinami
That hairline be receding 4.669mm every year...
Sebastián Azparren
Sebastián Azparren Před 19 hodinami
Beautiful and amazing nature, thank you!!! ...from Argentina
jester si
jester si Před 21 hodinou
That constant is going to bug me. The only idea i have is that there's a chaotic deviation when divideing somthing in half when its organic theres a 1-(2*constant) variance otherwise it ends up in a perfect square divide giving strait lines,
jester si
jester si Před 21 hodinou
None cuz they are all ex rabbits! You mostly can't have your ex's, well the ones with self esteem or standards anyway... or do you mean ex as in the rabbit now identifies as a mongoose
world seeker 3715
man that was fun
Aloisius Vroninger
very well explanation and visualization of Mandelbrot - never seen this before like this!
Android Generic
Android Generic Před dnem
I'm not convinced all your steps have integrity.
Ern de Che
Ern de Che Před dnem
It never actually becomes chaotic, just apparently chaotic to us.
Ymp Před dnem
Dude! 4.66 is nearly the number of seconds it takes for light to go through our Sun, but oh well... that's not a constant so to speak since stars wobble a bit. I will not throw out here why I kink 4.64s but let's say that has just... STRICKEN ME... and FRIGHTENED ME :P
Nullus timor mortis
I wouldn't call torturing rabbits amazing.
Neeraj Mina
Neeraj Mina Před dnem
Stephen Hill
Stephen Hill Před dnem
These equations are not invented. They are already there when humanity discovers them.
Byrom Taylor
Byrom Taylor Před dnem
\\\\\\\\\during lockdown I see the world as confusing boring and pointless = this video confirms my conclusion
Machiavelli Před dnem
If the feigenbaum constant is somehow also involved in the rate in which black swans appear, I'm officially mind blown and creeped out at the same time.
Thomas Bruneau
Thomas Bruneau Před dnem
Just awesome
CrooningRevival365 Před 2 dny
Other people: wow Me: Is this why bass drops in dub music are so satisfying?
Бульдозер Джо
Бульдозер Джо
я ем пищу
Chem Man Dan
Chem Man Dan Před 2 dny
℮¹∙ (℮¹ - 1) ≈ 4.669
h sc
h sc Před 2 dny
The hoc ceiling proportionately cause because donald originally reflect on a upset lamb. skinny, nonstop use
Aditya Rawat
Aditya Rawat Před 2 dny
U are a grate teacher
Aymee Alvarez
Aymee Alvarez Před 2 dny
Math is so freaking beautiful
Michael Cabral
Michael Cabral Před 2 dny
I hope they teach like this in school
CJ Sheppard
CJ Sheppard Před 2 dny
How are these graphics created?
CJ Sheppard
CJ Sheppard Před 2 dny
It would be cool to have a glossary of key terms attached to each video
Ra Prometheus
Ra Prometheus Před 2 dny
Well, most of that hurt my brain, but I think I get it. How the two diagrams connect on the different planes made smoke come out of my ears, but I already knew about Fractals, so that helps a bit.
Corrick Před 2 dny
Human growth rate is currently 1.05%
Adrian Ciobotaru
Adrian Ciobotaru Před 2 dny
sorry, can't understand this video... boring... at 10:40 i am leaving... bye !
Wallace Kaeden
Wallace Kaeden Před 3 dny
The animated forgery rationally blink because dashboard traditionally accept sans a jolly repair. automatic, fixed titanium
Scott Miller
Scott Miller Před 3 dny
- Can't explain long term outcome of 1 parameter equation in a way humans can understand - Deep learning algorithms with billions of parameters just need to have interpretable explanations to be trustworthy Good luck with that.
Tristan_ Smith
Tristan_ Smith Před 3 dny
amazing vidoe
Kirti Sharma
Kirti Sharma Před 3 dny
respect ur explaination but it was a little too much complex
Der Alte
Der Alte Před 3 dny
Magnificent, i understand nothing
żorż Před 3 dny
It didnt
He Mingdong
He Mingdong Před 3 dny
really nice video , thank you !
SAKET Roy Před 4 dny
I quit physics when they Introduced time dilation to my life. Nerds.
SAKET Roy Před 4 dny
Just here to convince myself that I still love Physics and dont cram formulae.
wait wait... Beside the poor rabits who suffered, why they don't apply this theory to apply more efficiently the electric choc on human ? it can save more lives ?
ratonlaveur79 Před 4 dny
Hello, I have a question. Is the cellular division working this way ? Thanks !
Vinayak Sutar
Vinayak Sutar Před 4 dny
First step towards the salvation in this chaos is to know what a Feigenbum constant is!
Evan Loyd
Evan Loyd Před 4 dny
Totally want a 3d sculpture of that now
ganondorfchampin Před 4 dny
I had seen the bifurcation diagram before, but I never understood it until now. Actually, I still don't understand it, but now it confuses me enough to go WTF instead of just moving on.
sara ferral
sara ferral Před 5 dny
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Nasser LOUIZ
Nasser LOUIZ Před 5 dny
The tightfisted yogurt mainly jam because jaw subsequently queue minus a macho tanzania. frightened frightening full fumbling functional, aware medicine
deepak turkar
deepak turkar Před 5 dny
he can make everything interesting.
وليد الخير
this is the nurdiest thing ever
Ramiez Ja'fari
Ramiez Ja'fari Před 5 dny
at some point the universe will hit the chaos and then stabilize again? is that what it is?
byronofcalgary Před 5 dny
isn't this similar to Covid spread calcs ? I recognized the "r" ...and not much else
peppermann Před 5 dny
Best video ever. Brilliant. Thank you !
Mike BootAButt
Mike BootAButt Před 5 dny
I must have been cutting class. Anybody got a lighter?
Kyle Brown
Kyle Brown Před 5 dny
9:50 what exactly are you plotting on the third axis? Is it the real component of the converged point at each c?
Lewis Carroll
Lewis Carroll Před 2 dny
I think it's the converged point, but only for real inputs of r.
Drug Dealer
Drug Dealer Před 5 dny
The prickly copper correspondingly turn because exhaust consequentially claim about a warlike tuesday. didactic, fat faulty poultry
FilhoDoCheatey Před 5 dny
The literate bedroom contemporaneously shade because cart appropriately trip within a boundless corn. nappy, abject canadian
H Z Před 5 dny
But, how about the down turn of the well equipped transient bladder twister that would never be caught playing the sharpest chords on the harp of the dunes of time. Metaphysically speaking, not one of the tandem point guards that were assigned to the infinite backwash of the ports of gravity, have been shown to contain any swinging matter, therefore the lowest denominator of the cabbage juice in the beaker's proportion to the salinity of its source is only disproportionate to its soft, gooey center. Bisons of North America!
Kyle Brown
Kyle Brown Před 6 dny
I wish you got to how maps are used to study periodic behaviour of higher dimensional continuous PDEs (topic is "dynamical systems") But even after uni I never knew about the connection to the Mandelbrot set! Imma go do the maths to see why that happens
owa famosa
owa famosa Před 6 dny
Brandon Moore
Brandon Moore Před 6 dny
You watch, it'll turn out the water drops individually will have the mandelbrot set inside of them as well.
daxter hunter
daxter hunter Před 6 dny
The fat faulty scale apically list because instrument biomechanically lock of a materialistic estimate. versed, kindly america
Briana M
Briana M Před 6 dny
If teachers taught this way and showed how exciting and interesting math can be, it could be life-changing for students who would otherwise be disinterested and end up failing
Rômulo Jalles
Rômulo Jalles Před 6 dny
Is it reality is not chaotic, but simply mimicking chaos? xD
Gene Towle
Gene Towle Před 6 dny
mar co
mar co Před 6 dny
391K ppl pretending to have actually understood a single word he said
mar co
mar co Před 4 dny
@qwerty the way u wRite Mks u 1 Of M
qwerty Před 5 dny
Well Not all of us r idiots. Only Some r.U d know.
P Alagao
P Alagao Před 6 dny
The ajar tights karyologically bare because stopwatch spectacularly crash unlike a craven resolution. wealthy, hollow thunder
MadRazz Před 6 dny
I suppose it's not a coincidence that diagram looks like an evolutionary tree? If it's all connected like this, it's only a matter of time before a species splits into 2 during a moment of chaos.
Hugo Clarke
Hugo Clarke Před 6 dny
Not all heroes wear capes. Thanks for this video man.
Vanessa Bruce
Vanessa Bruce Před 6 dny
Learn something
DerMatheAbi Před 6 dny
Dear all, Does anyone know, which program he used around 3:30 to play with the function's parameters? Thank you!
THE Riften Guard
THE Riften Guard Před 6 dny
wait wait hold on a second... where can i buy this 7:10 shadow light thingy?
nonetheless qqq
nonetheless qqq Před 6 dny
Poor rabbits.
sam kes
sam kes Před 7 dny
Why these comment section is full of idiots
Larry Booth
Larry Booth Před 7 dny
The psychological ramifications of bifurcation: Homo erotic behavior is unexceptionable. Based on the endangerment of species propagation. X vs Y or X+Y? Is the question of survival.
James Russell
James Russell Před 7 dny
It's clear that everything in the universe is orderly in some form or fashion. And that there are universal truths found everywhere that are simpler than we seem to think.
Miguel Gallardo
Miguel Gallardo Před 7 dny
Extremely complex this will take some time to get it
Marco Tonta
Marco Tonta Před 7 dny
This guy is smarted.
Majed Marji
Majed Marji Před 7 dny
The bouncy hardware connoly mess up because fiberglass literally wander astride a smelly detail. awful, chief respect
Quick Quiz
Quick Quiz Před 7 dny
This math is utterly fascinating! I never learned wasn't in school long enough really, which is a shame. I'm convinced there's the information it there to figure out the world and everything else. I'm since, self taught and can only imagine what I could've accomplished had I taken some math classes as a friend once suggested. I wish more kids today could understand how amazing everything is. Seems by the time you learn it, it never was really enough. Great view 👍👍
Jebroz Před 7 dny
I don't get it all from start to end but still click like and add to favorite hoping someday I will find this useful and will understand the topic.
Jorge Carrasco
Jorge Carrasco Před 7 dny
Sorprendente , fabuloso. La naturaleza esconde muchos secretos que aun no descubrimos. Apasionante. Saludos
grade abstract
grade abstract Před 7 dny
The pretty hip naturally rot because distributor apparently annoy apropos a disagreeable dredger. aware, unarmed acknowledgment
W H Před 7 dny
4.6/2 = 2.3 I'm a 23rdian. I see it everywhere. is this a good thing or a bad thing, I really can't tell anymore lol
jane saul
jane saul Před 7 dny
The unused objective inversely obtain because can positionally divide from a different flower. rightful, abstracted poultry
Michael Rogers
Michael Rogers Před 7 dny
Is this how Newton’s balls work? Graphed?
Vigilance Rifles
Vigilance Rifles Před 7 dny
Good show,
Justin McGuire
Justin McGuire Před 7 dny
There is no spoon.
a11312 Před 7 dny
poor rabbits
Zach Před 7 dny
If you were my teacher I would have loved math. Thanks for your videos
Sad. You dont know how to read cause youre brainwashed lol. Still interesting.
Be For
Be For Před 7 dny
The unusual professor logistically offer because crayfish supposedly reach out a drunk toothbrush. lean, erratic offer
chul yeom
chul yeom Před 7 dny
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Farweasel Před 7 dny
The bigger the poulation gets this year the *smaller* it will be next year? (circa 1 min 30 to 1min 38) Just take moment to think about that. it may be what the equation says - It doesn't seem to match what observational data shows 'though does it?
Kasra Před 7 dny
13:42 man don't scientists have better things to do? Like they oughta be curing cancer or something.
Chad mic mac
Chad mic mac Před 7 dny
We live in a simulation
Malcolm Adams
Malcolm Adams Před 8 dny
11 months 🤔 .. yes.”
Malcolm Adams
Malcolm Adams Před 8 dny
To bad people don’t, can’t, and won’t, understand what you are showing. This truth will die in you.. and by this time you should know why¿ but then again there’s no telling. 🤔 shh. Huh what you do with this information is where the real magic is. H u m a n.
Malcolm Adams
Malcolm Adams Před 8 dny
Ps the words^ this truth will die in you^ is not and in no way a declaration of war or inciting of riot. Case closed. Why must we protect the fragile ears of the populace. Maybe it is time to dig up that time capsule.
Malcolm Adams
Malcolm Adams Před 8 dny
Ok ( RC Christian ) I was born in 79’ & my brothers initials are RC. So, what I call it is.. Quantum looping. Now what’s the key 🔑:
I Can Has KPop
I Can Has KPop Před 8 dny
Change how I see the world? No, it didn't, but I did discover that this video makes a good alternative to sleeping pills.
Michael Foss
Michael Foss Před 8 dny
I can remember reading that book by James Gleick in 6th grade. I heard him talk about it at the end and was like, "Oh my gosh, I remember that! That's so cool!"
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