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

  visningar 7,811,730

Veritasium

10 månader sedan

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"

Kommentarer
Ranom Acc
Ranom Acc 2 minuter sedan
Me: understands less than 5% of what he said Also me: life changed
Bill Dickson
Bill Dickson 11 minuter sedan
Is there any relationship between the golden ratio, Pi and 4.669 ?
ycu4AB
ycu4AB 17 minuter sedan
what happens when you try to reverse engineer a behaviour with a different ratio of bifurcation distances? i.e. imagine a fittingly compressed bifurcation curve and then think about what the initial function has to be.
StunGaming
StunGaming 29 minuter sedan
wow it really changed my mind
Desirable Jodie
Desirable Jodie 40 minuter sedan
bi-fur-cation, I get it!
Jerry Peacock
Jerry Peacock 52 minuter sedan
2020 is chaotic enough, but this man is smart.
Jerry Peacock
Jerry Peacock 51 minut sedan
Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on
Desirable Jodie
Desirable Jodie 56 minuter sedan
0:30 explain this to my bunnies
Vau Bao
Vau Bao 3 timmar sedan
ఆ ఆi love u girl.
Tech Philosopher
Tech Philosopher 3 timmar sedan
*I need so much study 🙄 *
Nobu Tsuki
Nobu Tsuki 5 timmar sedan
It's turtles all the way down, the same way a brain cell looks exactly like the dark matter connections and pathways in our universe.
Dylan Dirkes
Dylan Dirkes 6 timmar sedan
I still see the world with my eyes.. this video is so fake smh
Ryan Kan
Ryan Kan 7 timmar sedan
mhm "active rabbits"
pennie schirz
pennie schirz 7 timmar sedan
"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)
Johnny Hammersticks
Johnny Hammersticks 8 timmar sedan
Mandelbrot on z axis looks like the universe a bit. I didn't understand HS algebra, but stuff I can see like this is totally different. Wow, this is amazing.
Angel Romana
Angel Romana 8 timmar sedan
Everyone here were gangsta till he turned the Mandelbrot-set 3D
Mahiya Jesi
Mahiya Jesi 9 timmar sedan
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
Mahiya Jesi
Mahiya Jesi 9 timmar sedan
The cracks on my phone look like this 😭
g k
g k 10 timmar sedan
When you say that rx grows exponentially, that in itself is a definite proof that you now nothing about math 👎
Miles Tinsley
Miles Tinsley 10 timmar sedan
3:27 AM Me: hunched over the sink My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!
funncubesde
funncubesde 10 timmar sedan
When I watched this video I though: I've seen lots of maths stuff... didnt change anything. EVERY TIME i turned on the sink, ever since and it started dripping I switch between chaotic and periodic. It really did change my life.... well a little bit.
aardvarkmcgillicuddy
aardvarkmcgillicuddy 11 timmar sedan
That dripping faucet reminded me of my prostate.....
AdryhZ
AdryhZ 12 timmar sedan
I dont think im fully understanding what Im seeing but I like it
Laura Hainke
Laura Hainke 13 timmar sedan
Shout out to everyone who is here because they were impressed but also bamboozled by James Gleick’s “Chaos” :D
Mo Ran
Mo Ran 14 timmar sedan
good
sprwil
sprwil 14 timmar sedan
Great👍 Thank you so much🤓
Taher Ali Patrawala
Taher Ali Patrawala 14 timmar sedan
30 January was my birthday!!😂
Tev J
Tev J 15 timmar sedan
It's like discovering some of the software God used to write the Universe.
Shane Davis
Shane Davis 15 timmar sedan
I love human beings!
Blake Terry
Blake Terry 15 timmar sedan
Dude, you break my brain.
Ash
Ash 17 timmar sedan
So this is how corona 1st wave 2nd wave 3rd wave 4th waves are predicted and govts around the world are forced to go on a merry-go-round lockdowns over and over around
Thu Moi
Thu Moi 17 timmar sedan
I love this movie.
AMclouds
AMclouds 18 timmar sedan
hey, can anyone help me simulate beautiful graphs like those with my own data? I mean most graph websites and software have ugly graphs
sean principi
sean principi 18 timmar sedan
WAYTOODANK
Andreas D
Andreas D 19 timmar sedan
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
Leo Schleck
Leo Schleck 20 timmar sedan
2020 is chaotic enough, but this man is smart.
Enm Tin
Enm Tin 20 timmar sedan
When someone loves you, the way they talk about you is different. You feel safe and comfortable.
Richard Beard
Richard Beard 21 timme sedan
based and epic
googhan
googhan 21 timme sedan
ok this was inspiring now Im gonna watch tiktok bella
barak shifman
barak shifman 21 timme sedan
Beautiful! Your best video 👏🏻👏🏻
Sareseras
Sareseras 22 timmar sedan
Is this where the hype for "the curve" is coming from? Tbf there was also this series which iIrc was on Netflix with a whole society relying on statistical curves too much like the Spartans did with oracles.
Tabitha Bailey
Tabitha Bailey 23 timmar sedan
Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on
kimtaetae_10
kimtaetae_10 16 timmar sedan
You: Copy and paste Me: go on
NerdzGetaway
NerdzGetaway Dag sedan
The cracks on my phone look like this 😭
Hobothesis
Hobothesis 3 timmar sedan
If you take a microscope and look at the even smaller cracks I'm sure it follows the same bifurcation
Nax Eni
Nax Eni Dag sedan
0:22 my love video :X.
Aneil Pokharel
Aneil Pokharel Dag sedan
What was illuminating for me is when you rotated the mandlebrot set with the population growth rate. Now it makes sense!
Gib Bogle
Gib Bogle Dag sedan
It is not possible to talk about the Mandelbrot set without using complex numbers.
The Linus
The Linus Dag sedan
4.669 is the tick rate of the RL server..?
Jose J. Breijo
Jose J. Breijo Dag sedan
(keanu voice): your content is incredibly fascinating! Beautiful approach 👏
Martha Simmons
Martha Simmons Dag sedan
So basically: everything in life follows a pattern, but that pattern is so subtle that most people will never notice unless they're specifically looking for it. At least, that's what I got out of it.
Vinyl Affair
Vinyl Affair Dag sedan
"Oh cool, the Mandelbrot-Set. I have seen that before." turns Mandelbrot-Set in 3D "What the ...?! That's illegal!"
Chase Green
Chase Green Dag sedan
Xrp ripple and bitcoin are making people rich af
Mark Henderson
Mark Henderson Dag sedan
The baptism of the holy spirit will do that first and more exactly, supernatural and science are coming together :) , the way it should be. Science started to have a an agenda with regards religion or God , the scientists started to become bias based instead of working from experimental proof.
Pedro Cytryn
Pedro Cytryn Dag sedan
Reality is made of non-linear patterns, and they repeat itself everywhere..."as above so below".fractals are the very pattern of energy that shapes matter. such great video and that axis rotation...speachless, gave me a whole new perspective on the mandelbrot set. thank you
curtis jaekl
curtis jaekl Dag sedan
has anyone read the paper posted by robert shaw that is listed in the video? just to confirm on page 15 there was a basic sketch of a mass stretching a string the releasing at the X0 of the system. for that equation what the x with two dots on top is the second prime of x correct and then the m with one dot is rounded or is that the prime of that number. I have done some internet research but cant find the answer, I will continue to try solving algebraically. the correct result in theory trend towards the chaotic entropy we learnt about in this video.
César David Zambrano Pereira
César David Zambrano Pereira Dag sedan
What calculation applications did you use on your mac?
Crystal Eye
Crystal Eye Dag sedan
nah... it didn't change anything with the way I see the world. sorry
skylander dad and skylander boy show skylanders
skylander dad and skylander boy show skylanders Dag sedan
The smarter i get, the dummer me is.all things being crazy.
My Ngui
My Ngui Dag sedan
Is my is my mother goose club out.
HealthCareForAll FiftySevenStates
HealthCareForAll FiftySevenStates Dag sedan
Has someone run an algorithm on the comments on this page? Because they are repeating under new names. I think someone is going to an EXTENSIVE effort to troll the point in the video.
Andy Hay.
Andy Hay. Dag sedan
Winner is left out of pocket. Sounds great.
josimar ruiz
josimar ruiz Dag sedan
x and x^2 are linearly independent. Yes, you can represent any function as a set of linearly independent functions. We can find a function for everything that can be said to be composed of linearly independent functions; let me save you some time and tell you that everything in this universe can be described as such. However, I am glad that people are at least thinking about this.
Kasper Aare Naicker
Kasper Aare Naicker Dag sedan
Very fascinating ! Thank you!
Joe Dance
Joe Dance Dag sedan
Enjoyed the video, but please stop saying everything is chaotic, or produces “chaos”! It is not chaotic, nor chaos. Everything you discussed demonstrated some kind of pattern. Even the periodic episodes of somewhat random-appearing behavior are part of a larger pattern. I also loved James Gleich, and physics, cosmology, ecology, etc. Some years ago, “chaos theory” led to the development of complex systems theory, which is fascinating, and more rigorous. Mathematics is everywhere, in the movements of traffic, crowds, flocks of birds and sheep, schools of fish; also in fluid flows, weather systems, climate change...It really is a small world after all. Best wishes for happy holidays. Please stay safe and healthy.
Lyudmila Osinina
Lyudmila Osinina Dag sedan
if they taught this kind of thing to kids in school im sure they would be 10x more interested in the subject. Its not something I would test them on, but just to show them how interesting and versatile math can be, I think it would get people a lot more motivated to learn.
Ta Thu
Ta Thu Dag sedan
I love this movie.
G G
G G Dag sedan
What’s the point of this video ?
Jasfras1
Jasfras1 Dag sedan
Soooooo ... Chaos is not Chaotic if you have ALL the beginning info !?
WroughtIron
WroughtIron Dag sedan
So my understanding is that rabbits must be eliminated before their reproduction breaks the game engine.
Seth The Cat
Seth The Cat Dag sedan
Figanbownd constant= controlled golden ratio maybe, not a mathematician by any means but really wanna wrap my head around more math
Mike Figget
Mike Figget Dag sedan
Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.
Hookairs
Hookairs Dag sedan
Thumbnail makes a cool album cover
Abinesh Anbazhagan
Abinesh Anbazhagan Dag sedan
If I had known how to do the simulations for rabbit population I would have preparing a manuscript on a peer reviewed journal😀. Great explanation.
kanedNunable
kanedNunable Dag sedan
my brain hurts now
Susan Moore
Susan Moore Dag sedan
This reminds me of “spooky action at a distance” Just rotating the Mandelbrot fractal in 3 dimensions was mind blowing... then the Feigenbaum constant...
Jessica Matos
Jessica Matos Dag sedan
Thats just amazing! thank you for putting it together!
Za Gran
Za Gran Dag sedan
/Говорит про спонсора видео/ Современные проблемы нуждаются в современном решение
Witold Geibig
Witold Geibig Dag sedan
"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)
st0ox
st0ox Dag sedan
The guy who programmed the universe used 4.669... as the seed for all random number generators, because he was lazy.
Xau Thu
Xau Thu Dag sedan
0:40 she is hot girl and sexygirl.
AKH1L
AKH1L Dag sedan
Complex than Dark web series
Groove Alex
Groove Alex Dag sedan
What if you teach a neural network to assume results with this ratio?
William Fabiano
William Fabiano Dag sedan
Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on
Tomás Hayes
Tomás Hayes Dag sedan
Sponsored by Fast Toasts
SDAD DSAD
SDAD DSAD Dag sedan
this is why I never change my point of view.
Alex T
Alex T Dag sedan
Took him exactly 58 seconds to throw me in the bushes with that theoretical maximum stuff. Maybe if I put my seat belt on. Nobody knew he was describing the coronavirus.
Alex T
Alex T 2 timmar sedan
@pennie schirz Now, you gotta splain that, Lucy.
pennie schirz
pennie schirz 7 timmar sedan
"There is no chaos and randomness in the world, there is only a non-open pattern." © Le Designer (I)
KNIRID Gaming
KNIRID Gaming Dag sedan
Teaching this to students only makes sense when you are not a STUDENT
Edi Majdani
Edi Majdani 2 dagar sedan
If u were my physics teache that would of be my favorite class
James Hanna
James Hanna 2 dagar sedan
So what you're saying is that the answer is 4.669? That is nowhere close to 42! I'm starting to think Adams made the whole thing up.
Randy Sokalofsky
Randy Sokalofsky 2 dagar sedan
Like children having hmmm moments in an adult world, science has it's hmmm moments when looking at God's creation equations
Hayato Tenryuu
Hayato Tenryuu 2 dagar sedan
I tend to think of things geometrically, so when you tell me that iterating a single hump function leads to a bifurcation series of individual humps, like that's the definition of iterating one hump. You have one hump. Then at the end of one hump, you do it again. Except per the quadratic equation and the natural existence of Phi, iterating one hump gives you three humps. Let's call first hump "-b", what comes next? (+/-) comes next. -b (+/-) the next term. So since we have one hump iterating, we have one hump joined to a positive and negative next hump. And that's bifurcation. That's literally the image you keep showing. And this also relates to transcendental numbers, which always come back up. The crazy thing is that transcendental numbers are an uncountably large infinite series of numbers.
Helder Almeida
Helder Almeida 2 dagar sedan
Okay we have now 8 billion people on earth and it's still growing not settling down
Linh Van
Linh Van 2 dagar sedan
I need boy friend
Stefan Leonte
Stefan Leonte 2 dagar sedan
Bad arab. You missed a spelling point.
F̶A̶L̶L̶ 17_2
F̶A̶L̶L̶ 17_2 2 dagar sedan
2020 is chaotic enough, but this man is smart.
F̶A̶L̶L̶ 17_2
F̶A̶L̶L̶ 17_2 2 dagar sedan
I wish this guy was my teacher
chicagotransam
chicagotransam 2 dagar sedan
How can I use this to win the Lotto? Thanks!
jyuy d
jyuy d 2 dagar sedan
3:27 AM Me: hunched over the sink My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!
FineLime
FineLime Dag sedan
At least change the words to make it look original and not copy pasted
C N
C N 2 dagar sedan
Sorry, you humans were not supposed to have stumbled upon this. Please wait while we update your server with a new patch, thank you for your patience -Robot Overlords
Sergio Maia
Sergio Maia 2 dagar sedan
Fantastic! A masterpiece. This is my favorite video among all the ones I have watched so far. I felt like researching it in more detail, but for lack of time could not do it. My favorite moment is when you wonder about the mistery of the constant..Why that value? Are we ever know enough to answer those question. Veritassium at his best! Excellent material for the classroom.
Han Tai
Han Tai 2 dagar sedan
Wow.
Amit Rana
Amit Rana 2 dagar sedan
This is literally the equation to why we have periods in our life where everything seems to be going smoothly and then chaotic. Anytime there's a consonant ratio between the values, you experience harmony; vice versa, anytime there's a dissonant ratio between the values, we experience chaos. There's also proof of this in the way we hear music, interestingly. If I were to record myself hitting a drum (tuned to any frequency) and then play it rapidly, I can make a constant stream of notes. If I speed it up fast enough, you begin to hear it sound like a vibration. Faster than that and it creates a note based on how fast or slow it's played. Is this feeling freaky yet? Imagine now adding another drum playing alongside the preexisting drum with another constant stream of notes. In the space it takes the 1st drummer to play 2 notes, the other is playing 3 giving us a 3:2 ratio. Speed these up together and we begin to hear an interval of a perfect 5th between the two notes. There is no limit to # of ratios (hemiolas). Once you add another player, there are now 3 notes heard and harmony is formed. So mathematically, percussionists make the world go 'round.
The Science Behind the Butterfly Effect
12:51
The Art of Code - Dylan Beattie
1:00:49
NDC Conferences
visningar 1,2mn
Shawn Mendes, Justin Bieber - Monster
3:04
ShawnMendesVEVO
visningar 45mn
Marty Lobdell - Study Less Study Smart
59:56
PierceCollegeDist11
visningar 8mn
Why do prime numbers make these spirals?
22:30
Cicada 3301: An Internet Mystery
17:54
The Infinite Pattern That Never Repeats
21:12
Why Machines That Bend Are Better
12:52
Veritasium
visningar 7mn
World's Lightest Solid!
12:02
Veritasium
visningar 24mn
I Waterproofed Myself With Aerogel!
12:22
Veritasium
visningar 27mn
Shawn Mendes, Justin Bieber - Monster
3:04
ShawnMendesVEVO
visningar 45mn
STÖRIG SPÖK-KOSTYM
3:35
IJustWantToBeCool
visningar 139tn
The Lizard Tier List
14:39
TierZoo
visningar 1mn
HOPPA BIL GENOM 2 HUSVAGNAR!!!
14:34
Marcus Dübois
visningar 71tn