#### Am Vor 2 years

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/ShawRober...

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:01... . 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"

## KOMMENTARE

## Daniel Smania

I am a mathematician, and I do study phenomena associated with the Feigenbaum constant. You did justice to the topic! Excellent video!

Vor year## John Gomez

@Veritasium 4.669/4 is roughly the golden ratio. 1.16725. If you multiply Phi*4 you'll get 4.672 which feels like some perfect heavenly number. It may be that 4.669 is nature's approximation of it, or some type of reflection in that processes in nature reflect some 99% of perfection. I'd wager people knew about this a long time ago and could be the kind of stuff that was lost in the Library of Alexandria. The secret book of John talks about Sophia which was kept secret by geometers to protect the ratio of perfection, and how the Demiurge was akin to nature attempting to take perfection onto itself but through chaos in ignorance, integrating imperfection to create reality and the disconnect between perspectives. It's kind of wild to me how the mind can interpret understanding of such deep concepts of its evolution, into parables like that, written thousands of years ago, and I'm glad that we've been able to name the math again and label terms that create what feels like a coherent history of people and our understanding of how knowledge is built and maintained throughout the generations. I'm hoping we can bridge the gap someday to quell the fear and anger in people of merely existing. Maybe we can build a better world that way.

Vor 7 Tage## Sergey Primak

X = 1-1/r

Vor Monat## Kinderschreck

@mindfieldproject must be chaotic

Vor Monat## Cristian R

@Svens Sipols good question i was thinking of this too. A thought that came to my mind was what happened to the universe during the Feigenbaum constant (in seconds of course, maybe months or even years. was there some kind of repeating?) Edit: another thought, is the unobservable universe outside of the mandelbrot set? just like how the number 1 is?

Vor 4 Monate## Svens Sipols

Would/is it aplying on cosmic expansion? Since cosmos is expanding we devide in subcosmic regeons (observable), then galaxies, and solar systems . Until it expands so far we we wont be able to see even nearest solar systems becouse of view limitatons. It turns out we can predict this by constant, thus the end of cosmo?

Vor 4 Monate## Taikamuna

My phone screen literally shattered in this shape

Vor 9 Monate## B

1.3kthliker

Vor Monat## Naruto

Sus

Vor 2 Monate## Fonroo

@Whimsical r/woooosh

Vor 2 Monate## Beauteeka

OMG just looked at my own screen

Vor 2 Monate## Powa

Idk put it in rice or smthn.

Vor 2 Monate## jemert96

*_rotates the Mandelbrot plot_* Everyone: "wait what's he doing" Me: "he's beginning to believe"

Vor 9 Monate## Laura Graves

There is no spoon. Just the Mandelbrot rotation.

Vor 28 Tage## Chris Pellegrino

“Now that’s the kind of comment I’ve not heard in a long time. A long time.”

Vor 2 Monate## carpballet

I’ve never seen the Mandelbrot set rotated. It really blew my tiny mind. I think chaos theory is somehow really important.

Vor 3 Monate## River Nickels

anti8

Vor 3 Monate## filip ao

Omg that’s exactly what I was thinking

Vor 3 Monate## Hidde

This concept is actually taught in engineering. Particularly in Control Engineering. It's taught because it gives a lot of intuition in nonlinear differential equations. These differential equations occur quite often in nature and in engineering problems when you have to model the dynamics of a system!

Vor 9 Monate## Magic Carp

Well said!

Vor 8 Tage## Ramaraksha

So much intelligence and brain power which all comes to a screeching halt once we get to religion Ancient people living under Kings/Dictators used such men as their template for God - Master/Slave religions - "we must get down on our knees, swear loyalty & obedience to the Master & only to this master. He will be pleased and GIVE us a life of comfort(Heaven)" Simple, primitive ideas from simple, primitive people frighteningly being followed by today's best of minds!

Vor 10 Tage## Satish Shetty

@Alberto Foti thankyou Alberto.

Vor 2 Monate## Alberto Foti

@Satish Shetty this equation is used as a demographic model. If you don't have a constraint, then you will have only births and no deaths. You need something to introduce a mortality rate, and it's this term 1-x that does this function. When the population grows over a certain threshold the deaths get bigger than births and the population goes down. the population can only became as big as the theoretical maximum, or approaching it

Vor 2 Monate## Satish Shetty

Hey, what's the limiting constraint 1-x. Can you explain it in a simple way.

Vor 2 Monate## Sara Ashley

I love that you mentioned that things like this should be taught to students. I completely agree!! Topics like this are why I started to be so interested in mathematics.

Vor 10 Monate## GÃMÉR X D King

this level of math is very high, most colleges dont cover highly complex theories, which will go over most of the people's head. I mean, most of us didnt even understand half the video evn after he explained it beautifully.

Vor 7 Tage## Lui Z

It should be taught *in the right way*. Many important things are taught in school, we just don't lean them. I only truly learned about the world and history and all the subjects I saw in school after I grew up, and it's not even a matter of teaching methods, it's just that a teen/child's mind is not ready to grasp that knowledge

Vor 9 Tage## Ramaraksha

So much intelligence, so much creativity and all that comes crashing down when we get to religion Billions follow Master/Slave religions - "we must get down on our knees, swear loyalty & obedience to the Master & only to this master, he will be pleased & keep us in comfort(heaven)" Simple, primitive ideas from simple primitive people being blindly followed by even the best of minds

Vor 10 Tage## Tanvi Sharma

Once the video reaches a certain rate of complexity, our brain starts to understand only periodic parts of it. Until it's all chaos and you throw your phone away.

Vor year## Abhinav AK

Tru tru 💀

Vor 3 Tage## Angry Young Man

@Pradeep kumar You have a Nice Imagination Power that You got my Point👍🙏

Vor 8 Tage## Pradeep kumar

@Angry Young Man Nice , Made me think over and over 😀

Vor 8 Tage## Sankeerthana9

L

Vor 8 Tage## Kayla Lyons

Why is the water bill so high? Me: Adjusting the tap into chaos

Vor 10 Monate## Stevo Robo

The Government+Nestle= Screw You. Pretty easy equation.

Vor 10 Tage## Cisco Ar

Nice lol

Vor Monat## DireWolf

@Zain Ahmed Peter baleish

Vor 3 Monate## Nerd#9347.

L.O.L, same.

Vor 4 Monate## Zain Ahmed

Chaos is a ladder

Vor 6 Monate## Wackeydelly

The reason that the bifurcation still happens when you change xn(1-xn) to sin(xn) is because that technically is your initial condition. The rate (r) is really what is important because this is just a fancy exponential function written in recursive form. The only condition on the initial condition is that it needs to cross the x axis at least twice (polynomial or trig function). Try doing Xn+1= r(xn^2-.01)

Vor 8 Monate## Shot Logic

between James Gleick's "Chaos" and Stephen Hawking's "A Brief History of Time" I've taken on a whole new perspective and appreciation for the ways in which the universe does its thing and the mathematics that we use to describe said thing. They're honestly pretty easy books to understand, Gleick and Hawking really did write their work in everyday-vernacular.

Vor 10 Monate## Rayo

@Ben Davis came to say this lol

Vor 6 Monate## Try again. K

@Ben Davis Yes, It was a very good read. But he started with a parabola and took a long time to explain it was used recursively. I would have like much more detail of chaos theory use in real life problems.

Vor 7 Monate## Ben Davis

@Try again. K Gotta say I like his writing style, though. It's more of a math history book than anything but for a general audience I wouldn't expect it to be too in depth. For me it was a good intro to "what is chaos theory and how did it begin?" However, I could see it being redundant if you've studied chaos theory at all and didn't care about the history of it as much as the math.

Vor 7 Monate## Try again. K

I found James Gleick's "Chaos" rather frustrating. His mathematical descriptions are imprecise because the boundary values are not stated and the iterative nature of the calculation is not expounded until a very long way through the book. He just concentrated on the parabolic equation. However it is fascinating.

Vor 7 Monate## Karl Davis

I love how this converges to the VALUE of the Mandlebrot set at each point. I've often seen the drawing of where the set has valid values, but never thought about the values it holds in those areas.

Vor 10 Monate## Lizard

I believe that in those videos of the Mandelbrot set where they zoom in for a long time, all the wild and crazy colors come from the value of the point as well. So visualizing the values in 3D space produces the logistic map with all sorts of chaotic lines, but visualizing the values with color produces a bunch of chaotic color patterns!

Vor 19 Tage## BelgianBush Rc

I am intelligent enough to find this interesting but not quite smart enough to fully understand... Great video!

Vor year## Joseph Smith

This is true for most of the ppl who don't know the math but understand the theory

Vor 3 Monate## N

Story of my life. A simpleton with a genius curiosity

Vor 4 Monate## Not Stazzmann

Literally the entire Veritasium channel.

Vor 6 Monate## Magic Carp

Learn every day!

Vor 7 Monate## Mike Bove

I don’zt fully understand yet, but I found 100 “thinks” to motivate me bro

Vor 7 Monate## Hrishikesh Rai

I’ve been studying mathematics all my life in school. Now in college, I’m doing a triple majors degree and one of the majors is math. Despite this, I’ve never felt an attachment or even a remote fascination for the subject. That is until I saw this video. This has sparked my interest and admiration for the subject. Kudos man for making such an amazing video!

Vor 3 Monate## Nathan Isaac

I love this channel, he explains stuff in a way that I can actually follow. I never would have understood anything like this were this to be taught in a classroom setting.

Vor 3 Monate## Dale Leighton

I was taught about chaos theory in high school at Qld Australia. I am very grateful to have had the teacher that I did for both our Extension Math classes AND our Physics classes. Thank you Ian Spence. 👍

Vor 10 Monate## Nicholas D

Dude you have THE BEST CONTENT in all of the internet. Period.

Vor 10 Monate## Matt

I love how throughout the video he's showing off his multimillion dollar house

Vor 2 Monate## Greg

Nice.

Vor 8 Monate## Variable

This feels like a window into a small part of how the universe works. Its kind of scary and exciting.

Vor year## Justin Anderson

Ad Veritasium, soldier.

Vor 21 Tag## Jeff Setto

@DoonTheGoonLive they probably just mean you see fractals and repeating patterns everywhere

Vor 21 Tag## multidolfan69

It is the equation that this universe was founded on. Nothing is immune, however there are several present constants that occur naturally and somewhat “resist” the equation. Humanity has the capability and capacity to be one of these constants.

Vor Monat## DoonTheGoonLive

What do u mean by “these” see equations everywhere or did you see the “mandablahblah” graph thingy everywhere.??

Vor Monat## Dylan Schmidt

@teun don't ever talk to my son or me again

Vor 3 Monate## Matt

Hey there! Huge, huge fan of your videos. I've learned more from you than any teacher taught me in school, so thank you for that! Anyway, I was just wondering if you or someone on your crew still has the 3D renders for the Mandelbrot set you guys did. Or even just some high res images... And if so if you'd be willing to share them with me (specifically the one from the top of the "needle" where you can see those secondary variations in 3D) because I'd like to avoid having to deal with graphing renders myself and I've got an idea for a project I'd really like to try. Thanks again for all the lessons

Vor 9 Monate## Noah Abrey

Hey Matt, I just looked into the description of the video, and it looks like there's a GitHub repo of both the initial graphs tool he was showing, and also the 3D render of the Mandelbrot set. It shouldn't be too hard to get running on your own computer.

Vor 8 Monate## Philip Crotts

Loved James Gleick’s books and Chaos is a great read. My favorite Math course in college was on fractals and chaos, learning about the Lorentz attractor, the Mandelbrot and Julia sets, and this equation about the period doubling bifurcation to chaos. Learning about fractal dimensions. Thanks so much for making your videos and keeping my love of mathematics going. Makes me want to look into chaos with all the other parabolic equations and check out feigenbaum’s constant. Truly great stuff, and definitely digging the recent trend of chaos which shows that even disorder is somehow strangely ordered adhering to prescribed properties mathematicians and physicists have been working out.

Vor 4 Monate## Rian Schoeman

James Gleick's book is really good. Once in a post office que I observed someone putting a fan on a scale. The reading bifurcated. I asked her to set the fan to a higher speed. The reading bifurcated again between four readings. I was blown away.

Vor Monat## Silca Lune

I've always called this The Conversion Points, when the parameters have so much changed that you have to totally change your behavior to continue it. It's not the same thing but to me it feel like being close to.

Vor 18 Tage## LC 7INEO

I found this incredibly fascinating... but understood incredibly little.

Vor 2 years## TheSheeplesShepherd

Omg same..also how I often feel after most Ve episodes

Vor 5 Monate## Sun Rider

@anamericangypsy That's generally the best way to learn towards something. 1. Look up what interests you 2. Write EVERYTHING that you don't understand down 3. Look up these things and reapply step 2. Afterwards you will have a map from your current knowledge to what you want to achieve.

Vor 5 Monate## janki prasad soni

Phew... I am not the only one here who understand little but feeling like have an exponential increase in my intelligence.

Vor 11 Monate## garet claborn

well it's basically like a cartoon snowball effect. the amount of snow you can pick up changes the bigger the ball gets. only the surface of the ball is also shedding snow off as it goes. so how much snow gets picked up for every 1 rotation keeps changing. this equation is like saying change is chaotic instead of in a linear pattern. at least pretty close to that

Vor 2 years## Alice Carroll

Wow! That’s actually one of the reasons I enjoy math - the same things come up everywhere? Thank you a lot for the video!

Vor 12 Tage## Steve RGR

You seriously blew my mind with this! I have never heard of it so far, yet when you told me the first thing jumping to my mind was the wave pendulum experiment. Isn’t that also an example of the sudden reorganisation after a period of chaos?

Vor 6 Monate## timchallenge

Just finished James Gleik's Chaos on Audible and man was it fascinating! Highly recommend!

Vor 6 Monate## Bruce Lawrence

So well done. A difficult subject made lucid with a great script and perfect visuals. Kudos.

Vor 10 Monate## Nitesh Jaswal

"How did I get to be 37 years old without hearing about the Feigenbaum constant", thank you for lowering that bound to at least a 24 year old. Your videos always leave me inspired!

Vor 2 years## Erity🏳️🌈⃠

@InCrIpTiOn 15 beat that

Vor 2 Monate## London Crotty

14 beat that

Vor 2 Monate## Atillatzke

I showed this video to my 1 year old cousin know he knows about it all

Vor 2 Monate## Scyth3934

@BorisTheBear 13

Vor 3 Monate## cosmnik

9

Vor 7 Monate## Alican Tuncel

Perfect. Amazing source of motivation to get into informatics, math, statistics, probability and game theory. The best. This video single-handedly spreads wisdom & helps humanity.

Vor 2 Monate## Ralph Beatty

Logistics curves were used to predict Covid numbers before there was a enough history to use geometric means. It also refines the R0 number (how contagious a disease is). I love this stuff! It is fascinating.!

Vor 4 Monate## A manuka

I can't even describe how amazed I am. Thank you for this video! It was a huge help with my studies and such an entertaintment!

Vor Monat## Tcloud

I think if you increase the frequency of a sine wave enough you get something like this pattern too which is pretty crazy as well.

Vor 9 Monate## Warren Chinn

Magnificent. I am a 53 year old professional entomologist and this is utterly pertinent to invertebrate population biology. You state you are 37 years old in this presentation and I feel very humbled. Thank you for restoring my confidence in a world that seems bent on science denial, superficiality and facebook banality. Please keep up these exceptional presentations of important and complex concepts in nature, top marks !

Vor year## Warren Chinn

@Raj Kishore New Zealand :)

Vor year## FlyingSavannahs

I gave you an up vote but you deserve to be recognized directly for such a pertinent comment. So, from a 60 year old physicist, I wholeheartedly say thanks!

Vor year## Grubbz

this man is capping hard fr. its Feigenbaum's second constant, numbers apply to a large class of dynamical systems (ie. a = 2.25029078...), like dripping faucets to population growth. dingus!

Vor year## Warren Chinn

@Sophie Jones I agree with everything you say - except the equilibrium part :)

Vor year## Sophie Jones

This only shows that no matter what we think the next generation somehow is doom, there always be good and bad and smart and stupid people in any generation thus everything will go towards equilibrium

Vor year## Ezie .Y.

I've subscribed to the channel for a while but haven't actually checked the videos up to now. It's incredibly magnificent how everything in this world seems to follow certain lines and is not random as we thought it is!

Vor 3 Monate## mihaly Kort

I went to the "Chaos Conference" at Sydney in (I think?) 87, met some pretty incredible physicists and mathematicians, and even got a couple of Autographs :) but mostly felt just awed that this was an interesting thing, and that I knew somehow it also was kind of important. B Mandelbrots lecture was lovely, but some of the different maths topics (from geometry obviously, but Prime number theory, Analytic and Discrete maths and biological mathematics. For me it was a memorable experience. So I get you, and I wish you more power to your arm, because yeah there's something compellingly beautiful and yet still mysterious. Good on you for your work, long may you continue and thanks!

Vor Monat## to2burger

Are the oscillating values on the Mandelbrot Set the boundaries that the equation bounces back and Roth between (I.e. the whole number value boundaries that the Zn+1 equation ends up going back to zero on) Or is it related to the number of data points that it takes the pattern to repeat itself again (I.e. like the rabbit model) ?

Vor 9 Monate## Peter Parsons

My lifelong interest in natural history often concluded in finding complex patterns in nature, but patterns for sure. Mandelson diagrams have always intrigued my interest and the universality you mention almost always presents at some point. I hope that your teaching, and inquiring mind helps to advance this area of learning. Great advancements in my lifetime, and many new questions. We are just starting , on the shoulders of giants.

Vor 7 Monate## BAgodmode

When you turned the Mandelbrot on it’s side to show the bifurcation, I’ll be honest, it blew my mind.

Vor year## CVN65

@bloodyassault6j The YT channel Mathologer has an excellent video on the genesis of the Mandelbrot set.

Vor 8 Monate## bloodyassault6j

can you explain how the mandelbrot become part of the bifurcation, or like where did the original mandelbrot get created from? the shape ? (does that make sense?)

Vor 8 Monate## CVN65

Boom.

Vor 8 Monate## buttafan

It reminded me of the scene from Contact when they're first analyzing the carrier waves and find a message ... except this message is like seeing the outstretched hand of The Great Simulator.

Vor 9 Monate## Vivek Joshi

Likewise

Vor 11 Monate## Jonsey

I simply love the way that you can explain farfetched concepts to me. Thank you.

Vor 8 Monate## MisterNewOutlook

Wow. Mitchell Feigenbaum is a name everyone should know. He should be right up there with Gauss and the rest. The Feigenbaum Constant is such an adaptable concept which reaches amazingly deep into the structure of systems. I never heard of him until this video and I thank you guys so much for presenting this. My knowledge and understanding of the world went up by a leap. At the same time, my awe and bewilderment.

Vor 8 Monate## Fudmottin

I would love to see the source code for the rotation of the Mandelbrot Set.

Vor 5 Monate## Tiberio Fanti

A great introduction to the theory. I've been playing around with these things since my dad took home for me and my brother our first 8086 PC. I played a lot with the algorithms described in Scientific American Computer Recreations, but never got the full picture as now. Well done!

Vor 8 Monate## Jess Lynne

The Mandelbrot Set in 3D is probably one of the coolest things I've ever seen

Vor 2 years## janki prasad soni

That blew my mind.

Vor 11 Monate## Merel Blom

The big part looks like the peach emoji 🍑

Vor year## TripleZ

@erteple it... Basically is lol

Vor year## Garv Chachan

@Jonny Rocket wow!!!u are awesome man😯😯😯😯

Vor year## Wellington Beef

Thanks for the suggestion. 😳

Vor year## one_cmnl

Taking Chaos Theory rn and this has brought so much light to many of my failed exercises. Incredible video thank you

Vor 3 Monate## Scope951

This was highly fascinating and entertaining. The data visuals are spectacular as is the narration. Thank you. I can’t stop watching your channel.

Vor 7 Monate## xionix4

I think you do it justice. I just saw something else on the internet reference the Feigenbaum constant what seems like a day or two ago. I wonder if it's causing its own awareness, lol. I find it pretty darn fascinating. Great job!

Vor 3 Monate## Sridana Windya

Poincare map is also an interesting graph. I did an experiment using driven pendulum in 1993 (my senior project). It exhibited chaos.

Vor 9 Monate## Rain The Vaporeon

I've not shown any interest in mathematics (or physics for that matter) for a long while, and this somehow sparked up my interest in it again, thanks. Really fascinating stuffs

Vor 5 Tage## Pulkit Agarawal

Dude! I love your content. Keep sharing such interesting mathematical stories.

Vor 9 Monate## aghni ermawati

I watch this video to try to understand my husband dissertation. He used this logistics function, bifurcation and chaos in mathematics banking fields. And yes, this is sooooo interesting!!

Vor 21 Tag## Sergey Mevsha

Congratulations! I'm from Ukraine! I really like your channel, it was always interesting to find answers to seemingly long-understood problems and phenomena. To see in a new way what you have to face all the time. Thank you for making such wonderful videos. I really want your channel to pay attention to what is happening in my country. Our talented people will be very grateful for your support. I have always believed that science is outside politics, but it is very closely intertwined in our lives in all its spheres.

Vor 4 Monate## Austen Alexander

Me: struggles with elementary algebra Verisatrium: Feigenbaum constant stays relative to the bifurcation diagram Me: go on

Vor 2 years## Dallas Mty

Lmao

Vor 9 Monate## Vivek Joshi

Woah... thats cool stuff 👍🏼👍🏼👍🏼

Vor 11 Monate## janki prasad soni

Hey I want to know who is veriasatrium out there? Sounds like Where is atrium.

Vor 11 Monate## janki prasad soni

@TwinbornMist Same here.

Vor 11 Monate## janki prasad soni

Same here. I didn't really understand anything but still continued to watch it because it seems like something interesting and fascinating is going on here. Thanks to Veritasium for bringing such mind blowing content.

Vor 11 Monate## Joao Batalha

Thanks for this and all your work. We need a world wide reform on the way we teach and the way the school system works. I love the fact that are people actively doing it right now. After 100 years it's about time

Vor 3 Monate## M. R. Magewright

Chaos is creative (perhaps I mean conductive or even subjectively beautiful) and order is an illusion. It seems to me that, there are only so many things necessary for a system to sustain itself and its' function. I am trying to think of the equation you've presented here in ways other than rabbits' notorious breeding habits. Such as applied to specific schools of thought or branches of science. I am trying to conceive the equation in a way that pertains to my abstract observations of the physical world. I can see many representations of the equilibrium you discuss, or at least I can conceive them. And I wonder if the equation expresses infinity; and if perhaps a closed system of an observable concept; that of an end. In this end, is represented (in terms of being assured by this formula) that it will inevitably fall into this sequence of equilibriums and chaotic states. I will look up more about chaos theory now. Sorry if I'm not making sense. I worked all day, studied all night and am about burned out. Goodnight and thanks for the video!

Vor 4 Monate## Bruce Foote

Your 3 dimensional animation of the rotating Mandelbrot Set graph conveys so very much information and complexity. Amazing!

Vor 23 Tage## Yo S.

Man since I've discovered this channel is like finally I'm relating to maths in any way. The fact that I'm understanding the implications of a equation (something I was taught to do mechanically at school without any purpose and hated later) feels like a big feat for me. As the humanist that I am (languages are my thing and did very bad at maths since I turned 14), now I sort of believe whatever truth there is about the universe, it will only be explained by maths. I've always made my own theories about it borrowing what I learned from philosophy, literature, history, mysticism, all based on natural languages and a different sort of abstract thinking, if you know what I mean... A little bit later I got interested in physics but still. But now this is BAHM. I'm always somehow deterministic when it comes to explaining human behaviour, nature, etc., and always believed there must be some underlying patterns, something really really basic yet complex that is within the core of everything that we know. I feel I'm closer to understanding, even if I must be incredibly far from it. But there's so much about maths I still don't know. I wish I had had better math teachers back in high school.

Vor 7 Monate## Andriy Predmyrskyy

As a control systems engineer, I've seen this behaviour before in several systems when control goes awry. Now that I know there might be something I can do about it, this opens up all sorts of possibilities to new control methods. I'm freaking out a little bit.

Vor 2 years## Sparky Dave

In theory correct, but you need a huge data set and non-trivial processing resources to see ‘where’ you are in the sequence. Not really PLC or control system server territory (yet) 😁

Vor 2 years## Loco Tx

I too was thinking . . "push all the buttons !!!!"

Vor 2 years## revenevan11

@brocktechnology I'm super excited for the possibilities of better control algorithms by using something analogous to the research in restabilizing heartbeats, the implications are awesome for aerospace engineering.

Vor 2 years## brocktechnology

I'm no engineer, but I'm right there with you. I was hit by the realization that this little bit of math is the reason PID is so difficult to do well.

Vor 2 years## revenevan11

Wow, you could control something back from the edge of chaos or even from already started chaotic behavior (like an airplane already entering an aerodynamic stall) using the methods that those scientists used on the rabbit hearts! I hope you're looking into that paper right now lol.

Vor 2 years## Adam

Hey! Does anybody know what software he used to make the population growth diagram and the bifrucation diagram?

Vor 4 Monate## 2424Lars

I've never heard of the Feigenbaum constant, yet its value feels eerily familiar...

Vor Monat## Take Guess

You are the man! Thanks so much for taking the time to do this!!! I love that you bring it back to education. You are onto one of my life goals... The education system need to be flipped on its head. We dont teach people to be smart, we teach them to memorize, which many people confuse with smart. We need original thinkers! Keep up the good work!!!

Vor 8 Monate## Saurabh Dwivedy

Thank you for giving a much better intuition for the Mandelbrot set than most other videos I found on YT so far

Vor 9 Monate## SomethingToJenga

"How did I get to be 37 years old without hearing about the Feigenbaum constant?" That is an extremely optimistic outlook on what 37-year-olds should be concerned about.

Vor 2 years## Dave Grvn

You've been seeing it your whole life SomethingToJenga, just you never knew people were using shorthand and just dropping the 4.6 part of 4.669

Vor year## Eric London

@GoGoCube> As well as actual wiper arms like on the windshield, some have them on the headlamps too. I thought a bit of overkill when I saw a classy car sport these as such.

Vor 2 years## GoGoCube

@SPB11 some germans cars like the early 2000 Audi TT and some SAAB cars had little hidden sprayers that popped out and sprayed the headlights with washer fluid.

Vor 2 years## Lonewolf Lolol

SPB11 what do you mean by that what can I gain from this if I decide to keep learning about it?

Vor 2 years## EmmaGao8

I love your video! They inspire me to think on these intriging topics! I wish they taught this at school

Vor 10 Monate## Shubham Gupta

Can you please provide information how did you model this? And the software that you are using. I'm always fascinated about such stimulations. Any help from your end is highly appreciated.

Vor 4 Monate## Lucas Walters

The fact that “chaos theory” is a real thing absolutely blows my mind. Even pure chaos can be mathematically modeled. Incredible.

Vor 5 Monate## Namakoro_osu

since the start of the pandemic i have come back to this video time and time again and it was the first video i watched of yours and every time i rewatched it i under stand just a little more thank you for making many complicated topics over the years bite size and understandable

Vor 2 Monate## Feynstein 100

Numberphile: Makes video about the Feigenbaum constant Veritasium: Makes video about the Feigenbaum constant but includes the z-axis

Vor 2 years## janki prasad soni

Veritasium: Also rotates the z axis

Vor 11 Monate## gbormann71

@Cezar Catalin The function of a single hump is the production of offspring.

Vor 2 years## Gottenhimfella

@SISSYPUSS Feigenbaum was not the only person back then to "find his bliss" that way. And I was not even a mathematician. Oh to be young again!

Vor 2 years## Jeffrey Sun

This is an amazing video, but I object somewhat to calling the Feigenbaum constant a "fundamental constant of nature." To me, fundamental constants of "nature" or "the universe" or "physics", like the Planck units, are still specific to our universe. The Feigenbaum constant, like e or pi, arises from simple rules that makes no reference to our universe. It is the same in any possible universe. It is a fundamental constant of mathematics.

Vor 2 Monate## dillon ahrens

This was crazy, did my best to grasp it, so much info. Loved it.

Vor 5 Monate## Sheena Abdul Basit

Bro you've done absolute justice with not only this equation but your videos do perfect justice with Maths.

Vor 7 Monate## Kian Ross

wouldnt this work with gravity, every action has an equal and opposite reaction? It explains how objects can collapse over time when a weight is added

Vor 2 Monate## Bonk

This man can calculate almost everything. The one thing he can't do is calculate a 16 : 9 aspect ratio.

Vor 2 years## janki prasad soni

What do you mean? 🤨I didn't get it

Vor 11 Monate## Kasper

Lol

Vor year## The Algorithm

@Adam Hanewald good for you

Vor year## santhosh kumar

@A RIs that a Sony... Phone???

Vor year## Ella Mentical

@i Believe your lies Ah! Me too!

Vor year## MouSeGrenadeXL

damn...just did this in my nonlinear mechanics class for engineering, really cool to see its applications in other fields!

Vor 6 Monate## foxhound MJ

fist thing that comes to my mind is to figure: 1- can you break down this equation to a differential equation and solve for the roots? 2- if a clean calculus method can't be found for the roots can you take a laplace transform or fourier transform instead of blindly fumbling with the equation in the time domain?

Vor 15 Tage## Data JY

💡 Best contemporary explanation to this pivotal concept! (origin, meaning, application) 👍🏻

Vor 8 Monate## Fraser Clark

Interesting, I agree with your views on teaching these things to children, perhaps it will make maths more appealing to them

Vor 8 Monate## Jessica Carter

Me: understands less than 5% of what he said Also me: life changed

Vor year## janki prasad soni

Me: Feeling exactly like you Me again: So, at last everywhere there is a chaos. The world is chaotic. Someone save me!

Vor 11 Monate## J A

Me who understood like 90% 😬

Vor year## TheBrickagon

@A M what do you mean by "was about time"? :)

Vor year## A M

@TheBrickagon Congrats, you figured you're a human being like the rest of your peers hence find similar behaviour with them! Was about time!

Vor year## Barry the Fish

Thats cause he's full of it

Vor year## John Caporaletti

I love your content man, this video in particular was fantastic

Vor 7 Monate## Christos Makriyannis

Nice video! What software do you use to estimate and plot?

Vor 9 Monate## Cosmic Ninja

5th time watching this video and it's easily one of my favorite physics/science/mindblow (idk what to call it honestly) videos ever on all of YouTube.

Vor 8 Monate## valterfcarvalho

I got into chaos theory when I was 15, by chance, when I joined a math club in scholl and there was a guy (one of my best friends today) that was really fascinated by it. A privilege, it's a wonderful world of patterns and numbers!

Vor Monat## EarthAsmr

You know the video is good when it’s 18:39 minutes long and you still didn’t want it to end

Vor 2 years## EarthAsmr

Darth Pro 😂👍🏻

Vor 2 years## Ристу Георгиев

I skipped most of it looking for the punchline.

Vor 2 years## Adolf Hitler

I did want it to end though, once the ad started playing

Vor 2 years## KillaahMusik

It felt like 4,669 minutes

Vor 2 years## Setsugen no ao

@Darth Pro same

Vor 2 years## strange420daze

Things like this make me think we might actually be in a simulation. Seems like we are starting to discover the shortcuts the computer has to take in order to handle processing the complexity of our simulation.

Vor 28 Tage## Terry Gilbert

I just kept thinking that it would be really interesting if this turned out to be a model of the expansion of the universe with an initial expansion and then switching to daughter universes budding off the edges.

Vor 8 Monate## Alex Haitch

Dude, the first time the fractal was rotated to reveal the graph absolutely BLEW my mind!!! Love this channel!

Vor 7 Monate## Bruce Foote

It is amazing to me that your simple population equation ties in directly to the Mandelbrot Set. My heart attack ties in to the chaos of Rabbit population figures. That the density of squirrels and oak tree nuts year after year, and the years of Cicada dormancy both coincident with primary numbers!!!

Vor 23 Tage## Peter Zoghbi

what software are you using to plot the equation ? awesome video by the way

Vor 2 Monate## Keyvan Malaie

That was really a fantastic! Thank you!! I got scared seeing the bifurcation for the first time!

Vor 22 Tage## Darren Irwin

Fascinating! Thank you for this wonderful video.

Vor Monat## Karen Miller

Great video thank You for your work and time by explaining this

Vor 8 Monate## Harsha Vardhan

From this video, one thing I understood clearly is that smart people actually deserve a house like that

Vor year## janki prasad soni

Today, I got to know that the symbol "Ans" in calculators means Answer.

Vor 11 Monate## Man Chul

Are you sure? But American protestors don't seem to agree with you

Vor year## Jacobthejewela

Can't you guys just disagree with someone without spasing out? You might get more likes with the name calling and one-liners but anyone reading this thread critically is going to side with the guy that's not acting like a child. Maybe your emotional reactions are doing your cause more harm than good.

Vor year## Leif

Why do smart people deserve it more than others?

Vor year## Tekanova

Don't fuss too much, it's a rental.

Vor year## Bouncy ._.

This is awesome. I Love science and thats why i study this. I've never heard about all the stuff on your Channel. Its awesome and interesting!

Vor 3 Monate## P Uday Shankar

Your videos never failed to make me think about what is the purpose of this universe.. why is it there and how it works so perfectly without anyone controlling it..

Vor 9 Tage## J. V.

my dear youtuber, i love your stuff. the. ice thing about some of your clips is, that i can follow and understand the context whilst watching. but i can not describe it to someone else the next day. wich only means, you are able to describe something very complex in an easy way.

Vor 7 Monate## Jesse Underwooh

So would you consider this to have the same effects as turbulent flow, the energy dissipates in both along with being random

Vor 7 Monate## Voldemort

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.

Vor year## marshall bruce

I think there is still one horcrux left.

Vor year## kanedNunable

showing that the useless algebra you do can be put to use. i learn much better if i can see why something happens and what its uses are.

Vor year## CyPhi68

These comments are very interesting. I'm 74. 20 years ago I took a buy out package and got a teaching license. I was in IT at the time in a Forest Products company. I was a Forestry major. Taught one half semester at a public school and quit. Too much politics, teaching to the test. Then taught at a private school for 4 years, math and science. I learned from my students that they have to be engaged. I allowed open notes tests, anything in their own hand or a handout I had given them. No photocopies or printouts. I allowed them to do experiments and tell the class what they found. Present in pairs and that pair picks the next pair, not the teacher. I made crosswords (15 words) for science quizzes. 2 points per word, first person gets 30 points, next two get 29 points, next 3, 28 points and so on. That was open book. But if you didn't read the material, those who had would beat you because they would finish sooner and get more points. Since then, I have been tutoring math and science at a community college, past 10 years. Apparently I do well. I have had students who will not take a course unless I can tutor them. Another who told the teacher to not explain things to her because I did it better. I appreciate that but I am too old to be vain. Just so I can help. Teachers make a difference, but educators (the ones with initials behind their names) seem take the fun out of teaching and learning.

Vor year## TheDallyboor

I think that showing the kids something so complex as the Mandelbrot set is gonna have a great outcome for kids talented for maths, but it will kick the non-math kids off the cliff. IMO not everyone has a brain for understanding math, for understanding what hides behind all the numbers and letters, all the equations, etc. If one cannot see the impact of all the basics of math in real world, it would be kinda weird to teach them stuff like the Mandelbrot set, even if it's super interesting for us. That is maybe the reason why a huge part of learning math at school is memorizing - formulas, multipliers, discriminant, etc...because everyone can memorize if they try hard, but not everyone can properly understand math with just like 3 hours of math a week, and at home there's nobody to help them understand, but they can practice memorizing it by themselves. So the system is adjusted so all the kids are gonna get a piece of "math". If we want to show the kids how math is fascinating, we must lead them to understand the basics of math, both at school and out of it. But I'm not the teaching expert, just my opp.

Vor year## Blade Runner

But you would have to do that in the first few years, before digital games ensnare them and will stifle interest in complex matters in a lot of kids (mainly boys, to be honest).

Vor year## Fabio Cury Pagliuca

Cool! Any chance this is a valeu related to golden ratio? Nature has a "tolerance" of nearly 3x times it's growth rate(set as golden ratio), before reaching chaos?

Vor 4 Monate## Devisidev

You were 37 when you learned about it, I'm 17. Youre doing good, you're teaching as I agree we all should be. This is incredibly fascinating.

Vor 2 Monate## AJ B

This reminds me of how a quantum object jumps instantaneously between different quantum states/positions

Vor 8 Monate## Dillon Gay

If my math teacher showed me this I would have been a great student. Instead we covered material like cattle for tests with no idea as to how the math relates to its application. When will I use this I asked. On the test he said. I am also very passionate about this and the Fibonacci sequence. Thank you for a great video!

Vor Monat## blobishly Belfer

thanks for showing me that as a child i had absolutely no chance of predicting when a water drop will drop.

Vor year## Arindam

@h b my god I'm the epitome of sin

Vor year## SuperMrDelgado

I guess you didn't pay attention to the video.

Vor year## oumar diop

@h b will that help me predict the water drops?

Vor year## Junior von Claire

@Plinio Averbach When a water droplet would fall?

Vor year## Angel Basaldua

Droping the water drop?

Vor year## john

I can’t believe how simple but complex this is at the same time

Vor 10 Monate