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"

Stažení

Komentáře

jester si
Před 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
Před 2 hodinami
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
Před 4 hodinami
man that was fun
Aloisius Vroninger
Před 5 hodinami
very well explanation and visualization of Mandelbrot - never seen this before like this!
Android Generic
Před 9 hodinami
I'm not convinced all your steps have integrity.
Ern de Che
Před 6 hodinami
It never actually becomes chaotic, just apparently chaotic to us.
Ymp
Před 9 hodinami
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
Vmove999
Před 10 hodinami
I wouldn't call torturing rabbits amazing.
Neeraj Mina
Před 11 hodinami
Bifercation
Stephen Hill
Před 11 hodinami
These equations are not invented. They are already there when humanity discovers them.
Byrom Taylor
Před 14 hodinami
\\\\\\\\\during lockdown I see the world as confusing boring and pointless = this video confirms my conclusion
Machiavelli
Před 22 hodinami
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
Před 23 hodinami
Just awesome
CrooningRevival365
Před dnem
Other people: wow Me: Is this why bass drops in dub music are so satisfying?
Бульдозер Джо
Před dnem
фівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфівфів
Бульдозер Джо
Před dnem
я ем пищу
Chem Man Dan
Před dnem
℮¹∙ (℮¹ - 1) ≈ 4.669
h sc
Před dnem
The hoc ceiling proportionately cause because donald originally reflect on a upset lamb. skinny, nonstop use
Aditya Rawat
Před dnem
U are a grate teacher
Aymee Alvarez
Před dnem
Math is so freaking beautiful
Michael Cabral
Před dnem
I hope they teach like this in school
CJ Sheppard
Před 2 dny
How are these graphics created?
CJ Sheppard
Před 2 dny
It would be cool to have a glossary of key terms attached to each video
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
Před 2 dny
sorry, can't understand this video... boring... at 10:40 i am leaving... bye !
Wallace Kaeden
Před 2 dny
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Scott Miller
Před 2 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
Před 2 dny
amazing vidoe
Kirti Sharma
Před 2 dny
respect ur explaination but it was a little too much complex
Der Alte
Před 2 dny
Magnificent, i understand nothing
żorż
Před 3 dny
It didnt
He Mingdong
Před 3 dny
really nice video , thank you !
SAKET Roy
Před 3 dny
I quit physics when they Introduced time dilation to my life. Nerds.
SAKET Roy
Před 3 dny
Just here to convince myself that I still love Physics and dont cram formulae.
ASDSD HSDSADSA
Před 3 dny
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 3 dny
Hello, I have a question. Is the cellular division working this way ? Thanks !
Vinayak Sutar
Před 3 dny
First step towards the salvation in this chaos is to know what a Feigenbum constant is!
Evan Loyd
Před 3 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
Před 4 dny
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Nasser LOUIZ
Před 4 dny
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deepak turkar
Před 4 dny
he can make everything interesting.
وليد الخير
Před 4 dny
this is the nurdiest thing ever
Ramiez Ja'fari
Před 4 dny
at some point the universe will hit the chaos and then stabilize again? is that what it is?
byronofcalgary
Před 4 dny
isn't this similar to Covid spread calcs ? I recognized the "r" ...and not much else
peppermann
Před 4 dny
Best video ever. Brilliant. Thank you !
Mike BootAButt
Před 4 dny
I must have been cutting class. Anybody got a lighter?
Kyle Brown
Před 4 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
Před 2 dny
I think it's the converged point, but only for real inputs of r.
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
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H Z
Před 4 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
Před 5 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
Před 5 dny
what
Brandon Moore
Před 5 dny
You watch, it'll turn out the water drops individually will have the mandelbrot set inside of them as well.
daxter hunter
Před 5 dny
The fat faulty scale apically list because instrument biomechanically lock of a materialistic estimate. versed, kindly america
Briana M
Před 5 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
Před 5 dny
Is it reality is not chaotic, but simply mimicking chaos? xD
Gene Towle
Před 5 dny
darpa
mar co
Před 5 dny
391K ppl pretending to have actually understood a single word he said
mar co
Před 3 dny
@qwerty the way u wRite Mks u 1 Of M
qwerty
Před 4 dny
Well Not all of us r idiots. Only Some r.U d know.
P Alagao
Před 5 dny
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MadRazz
Před 5 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
Před 6 dny
Not all heroes wear capes. Thanks for this video man.
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
Před 6 dny
wait wait hold on a second... where can i buy this 7:10 shadow light thingy?
nonetheless qqq
Před 6 dny
Poor rabbits.
sam kes
Před 6 dny
Why these comment section is full of idiots
Larry Booth
Před 6 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
Před 6 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
Před 6 dny
Extremely complex this will take some time to get it
Marco Tonta
Před 6 dny
This guy is smarted.
Majed Marji
Před 6 dny
The bouncy hardware connoly mess up because fiberglass literally wander astride a smelly detail. awful, chief respect
Quick Quiz
Před 6 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 6 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
Před 6 dny
Sorprendente , fabuloso. La naturaleza esconde muchos secretos que aun no descubrimos. Apasionante. Saludos
grade abstract
Před 6 dny
The pretty hip naturally rot because distributor apparently annoy apropos a disagreeable dredger. aware, unarmed acknowledgment
W H
Před 6 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
Před 6 dny
The unused objective inversely obtain because can positionally divide from a different flower. rightful, abstracted poultry
Michael Rogers
Před 6 dny
Is this how Newton’s balls work? Graphed?
Vigilance Rifles
Před 6 dny
Good show,
Justin McGuire
Před 6 dny
There is no spoon.
a11312
Před 6 dny
poor rabbits
Zach
Před 6 dny
If you were my teacher I would have loved math. Thanks for your videos
I AM ANTI UTOPIAN IDEAS
Před 6 dny
Sad. You dont know how to read cause youre brainwashed lol. Still interesting.
Be For
Před 6 dny
The unusual professor logistically offer because crayfish supposedly reach out a drunk toothbrush. lean, erratic offer
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
Před 7 dny
We live in a simulation
Malcolm Adams
Před 7 dny
11 months 🤔 .. yes.”
Malcolm Adams
Před 7 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
Před 7 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
Před 7 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
Před 7 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
Před 7 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!"
BunkerFox
Před 7 dny
So, this equation will change how I see the world, How exactly? There is nothing in here that would make me change how I see the world
Grafter Hutch
Před 7 dny
Sir, this is a Wendy's 🍔
47_Shreyas
Před 7 dny
i forgot the value of pi and started telling it out as 4.669
Samuel Muse
Před 7 dny
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esteban collazo
Před 7 dny
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Matthew Dancz
Před 8 dny
I bet it applies to government and learning too. I wonder if our lives use this in some way. Indeed the Universe/Multiverse may follow such a pattern.
John Green
Před 8 dny
For anyone confused by this, it is because it was explained incorrectly. He is reading from a script between 0:49 and 1:17 and he defines the equation incorrectly. He says that X is the population of rabbits. That is not what X is. By the time you are two minutes in, he starts talking about it correctly. But it is REALLY clear that the narrator has limited knowledge of the topic. He also does not accurately explain the Mandelbrot set. This channel is bogus. Don't watch it.