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/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"

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1 май 2024

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Комментарии : 26 тыс.

@tanvisharma6903 3 года назад

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.

@realdanrusso 3 года назад

yeah i made it 8 minutes in --with so much struggle-- and then blew up

@ashfujiyama 3 года назад

this is such an underrated joke

@caturlifelive 3 года назад

@gingaming_gg 3 года назад

Pretty much 😂😂😂

@depressedguy9467 3 года назад

Go back

@AustenAlexander 4 года назад

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

@nickreed7277 4 года назад

Damn dude. your elementary had algebra? i didnt get to that till highschool

@Matt_10203 4 года назад

@@nickreed7277 or he means that it is elementary level algebra, not in relation to schooling, just that he struggles to understand the basics of algebra

@Edlundd 4 года назад

Bro I dont even know what algebra means

@JoeyLovesTrains 4 года назад

Lol I got algebra in 8th grade in Middle school But my class was the only one, everyone else had pre-Algebra

@luppa79 4 года назад

Verisatrium :)

@brucefoote540 Год назад

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

@ingridfong-daley5899 5 месяцев назад

YES! Thank you for such well-constructed visualisations. They really are like compact little gold mines of information. :)

@3orM00Rrecharacters 5 месяцев назад

I’m an artist and took screenshots of the set graph and logical equation as inspiration. Data really is beautiful.

@ingridfong-daley5899 5 месяцев назад

OMG i took screenshots as well :) Agreed--data IS lovely.@@3orM00Rrecharacters

@HiManLOL 5 месяцев назад

people out there proving existance of god with Mandelbrot fractal

@convolutionality 4 месяца назад

its so pretty my inspiration too

@madeeb04 Год назад

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

@entropy_7827 3 года назад

Everyone's gangsta until Mandelbrot set gets rotated on the Z axis.

@FunTheMentalist 3 года назад

when he rotated the Mandelbrotset on the z axis, i felt that

@kumarsaieshrane9692 3 года назад

😂😂😂😂

@masterpsk 3 года назад

I did the "Keanu whoa" follow by a long "Duuuude!"

@gangsta6730 3 года назад

I was like "hol up-"

@eusebiorozco 3 года назад

Hahahahaha

@ColorwaveCraftsCo 3 года назад

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

@erteple2647 3 года назад

looks like a deformed pringle

@benhsuan4817 3 года назад

That and the "shadow" of a 4-dimensional cube passing through 3 dimensional space are the coolest mathematical animations I've seen. Matt parker shows it at the end of his talk at the Royal Institute if you're interested.

@mizomint4197 3 года назад

But... Humans can't see in 3D... So... Have you really seen it?

@bestawdomx6835 3 года назад

@@erteple2647 there is infinite?

@steveskeletonne-7394 3 года назад

ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-9U0XVdvQwAI.html This is essentially just a bunch of 3D fractals.

@joekelley5121 Год назад

I've had courses in Algebra, Calculus and Trigonometry, but never really had these concepts connected to actual real-world phenomena, so it always felt very... mechanical, very transactional. If they incorporated these concepts into the teaching, I believe it would make it much more relatable during the process.

@mikeinjapan2004 5 месяцев назад

Good point. But there are people who can actually connect those things naturally. I think this is also a skill on its own - we don't need to be thought because we see those patterns interacting each other and what have presented seems to be trivial...

@stiefjac5082 5 месяцев назад

100% i always thought that we would have leaps and bounds of breakthroughs in understanding the entire structure of the universe if we taught students in school basic math... and then showed them crazy concepts like these in the hopes that one of the billions of people on the earth will see them and go "huh that reminds me of x, what if we apply it here?" rather than pushing them through advanced mathematics to get degrees not only that but if you look up slow motion explosions on youtube and look closely the inital explosion looks like the mandelbrot set, and you can see that as it expands there are little bits of contraction in every single explosion if you take it frame by frame i watched this video when it came out 3 years ago and i've been obsessed with the concept ever since

@ADUAquascaping 4 месяца назад

@@mikeinjapan2004You probably notice all of the 25+ functions within plasma/flame 😮😂

@va941 4 месяца назад

Guess you never did psychedelics while in school then😂😂😂

@piercelane7757 3 месяца назад

A lot of this video is centered in something you might find in a numerical analysis class. I just took one in college and we went over a lot of this kinda stuff.

@zanityedpo1398 10 месяцев назад

When I was young, I always paid attention to my leaky faucets. I would mess with the flow since we were already wasting water, and I noticed this happening. Warms my heart to see it explained 💜

@strayspark1967 8 месяцев назад

i've had a similar experience, now explained 30 years later......strange world we live in, everything makes sense, eventually

@dmajorvgm8735 5 месяцев назад

The video didn’t really explain the behaviour though, it just made an observation/comparison to the mathematics they were talking about. I’d be interested in a more in depth video that actually explains why we see this behaviour so often

@nu1x Месяц назад

@@dmajorvgm8735 Well, noone knows WHY, people just noticed where it matches the algorithm. And why may be, I strongly suspect, some extremely fundamental basis on which the whole reality has existence, hence why this video is quite startling.

@BAgodmode 2 года назад

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

@jingalls9142 2 года назад

That one made me stand up an pace frantically for awhile....mind blown..

@shadeop6773 2 года назад

@@jingalls9142 same..... It blew my mind.

@asparagii 2 года назад

yeah that was awesome

@carriersignal 2 года назад

Same here. Had to stop it and sit back in my chair. Perhaps this is well known, but this is the first time I have ever heard of it.

@r0flcats 2 года назад

Its now my wallpaper!!! That image its insane

@feynstein1004 4 года назад

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

@unathimatu 4 года назад

it was a bifurcation

@BinyaminTsadikBenMalka 4 года назад

@@unathimatu lol, perfect response dude!

@BasiC7786 4 года назад

and then there's 3blue1brown telling you what PI has to do with all of this

@cezarcatalin1406 4 года назад

Feigenbaum constant: Works for all recurrences that come from functions with a single hump. A mathematician: Well, we have to demonstrate that A computer scientist: Give me the Summit supercomputer for a few days to find a counterexample

@larrysal8866 4 года назад

_mind blow_

@maegodragon Год назад

Only got to 5 mins and 18secs and already getting Heart Flutter! This video animations, graphing bifurcations, and the questions you pose prior to clear explanation is absolutely AWESOME! Thanks for the Thrills!

@marco-salfi Год назад

You a rabbit by any chance

@hugojj101 Год назад

You're heart chaotically fibrillated, you maybe dying haha. Nah that's mad though. If you're heart did actually double beat, that was literally an example of the video. So strange, and even stranger that complex numbers that exist on a plane we can't see are linked to all our hearts and the rest. One day we'll understand maybe. hah

@ainzulgone492 Месяц назад

Who's here in 2024 after the 37 video and noticed he said 37 as a random example 😅

@Mr_Noob-jp8nv 2 дня назад

Oh yeah, at 6:12

@Chord_ 2 года назад

"I'm so excited about chaos" -man one month into 2020

@maumau9466 2 года назад

Lmao😂😂😂

@norpriest521 2 года назад

@@maumau9466 What that means

@starryepidemic2532 2 года назад

@@norpriest521 it means laughing my ..... Off and no im not gonna fill in the blanks

@koborkutya7338 2 года назад

Well, it just tells us someone is messing with the parameters big time.

@MrSleepyweezul 2 года назад

When things are chaotic, you focus on chaos. And when you focus long and hard enough, even chaos can make sense.

@garfieldturismo 4 года назад

Everyone here were gangsta till he turned the Mandelbrot-set 3D

@cfneal1459 4 года назад

Explain? Please.

@doctorquantum3364 4 года назад

@@cfneal1459 r/woosh

@jinx5349 4 года назад

@@doctorquantum3364 you can't woosh someone for wanting an explanation.. 🙄

@rohangaikwad255 4 года назад

Hahaha

@maxlank539 4 года назад

I'm dead 😂😂😂😂

@falcxne Год назад

For anyone wanting to study the math of this, I recommend Steven Strogatz - Nonlinear Dynamics and Chaos. That was the textbook I used in undergrad.

@simrans3675 Год назад

So, basically, 'Chaos' is a misnomer now. There is clear method and math to the madness. Are we really living in a simulation :-)? Sometimes, it fascinates me to see all the advancements made in math, science. probability. stats etc with a simple thesis to put some structure/framework to quantify the world around us. It has helped us explain a few phenomenons, create products, even predict stock prices, human behavior (looking at patterns and trends etc) but the other part of me is conflicted - for life and its energies cant be modeled. It's too fascinating to be modeled out and the vastness of the universe and my spiritual beliefs are a complete anti-thesis to my scientific side. Heck, even science is ever changing - now, we are discovering qubits - particles that carry both -ve and +ve charges, which has deep implication to our view of physics and the world around us! While amazing, how much can humans really 'figure out' vs realizing there is something more to life that what even our more prolific attempts at math/AI/ML will ever get us to.. Or, perhaps, there isnt a higher power :-)?

@BanditMatt Год назад

Currently writing a report on chaotic behaviours and bifurcations, remembered this video existed and im so grateful now

@roshnirana2098 4 года назад

2019:- so this is aerogel 2020:- let's throw a little chaos at children and each other

@AngelOrtiz-wt7xt 4 года назад

Roshni Rana aqq msm

@zperdek 4 года назад

Chaos is magic.

@PavR376 4 года назад

Hey we have the same last name, first time I've meet one online

@user-pj8mt2kd4v 3 года назад

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@blobishlybelfer2717 3 года назад

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

@K3zz21 3 года назад

"when a water will drop" a SINGLE water

@who-ow5ix 3 года назад

😂😂

@plaverbach 3 года назад

@@K3zz21 When the water would drop?

@zacharyhall7466 3 года назад

Chaos theory?

@haydenbellis3047 3 года назад

.Turn to United Brethren Church. Using the Lords name in vain is a sin and so is cursing upon your enemies. And so is saying anything hateful, premarital sex and lust are all sins..⁰

@Peace2051 10 месяцев назад

Thank you for making some fundamental mysteries of math/nature at least approachable if not fully understandable to the general public. Great job!

@Sagitarria Год назад

You really did a good job with this one. This is something that’s been fascinating to me for a long time, and there was even a point a few years ago when I was trying to explain to my mathematical friends, the connections between the logistic map and the Mandelbrot set and they didn’t believe me! This stuff seems so fundamental, but it doesn’t seem like it’s tot as a unifying principle when it could be. It’s just nice to see somebody acknowledge all of these different pieces of the puzzle so thank you and thank you for making some thing I can .2.

@youmaybebusy 4 года назад

"Oh cool, the Mandelbrot-Set. I have seen that before." *turns Mandelbrot-Set in 3D* "What the ...?! That's illegal!"

@DrIridium 4 года назад

haha same

@scurvofpcp 4 года назад

I know, right

@IRuinEvrything 4 года назад

relatable

@smoothe14 4 года назад

This is getting out of hand, now there’s two of them... wait four of them. Hold up. Eight of them... wtf a chaotic number set of them??!? This really is getting out of hand. Oh wait no just two of them.

@Uberkist 4 года назад

mandelbulbs are gunna blow you away bro

@edstervedster 4 года назад

6:40 When the animation showed the Mandelbrot set being related to the bifurcation diagram my mind was blown...

@elee9056 4 года назад

edstervedster I WANT THAT MODEL AS A CHANDELIER. SO. BAD.

@carloshogar2 4 года назад

Same here. I am fascinated by fractals and never knew this relationship

@airpolygon2714 4 года назад

@@elee9056 you should make that idea a reality! I'd buy two

@rianby64 4 года назад

The same happened to me! not sure if really they're related... must rewind and check it again.

@Cloud7050 4 года назад

Crowdsourceeee

@amanuka291 Год назад

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!

@jeff_tj Год назад

That book is amazing - and you have done it justice. That 3d graph was awesome!

@jawadfarrukh6736 Год назад

Do you know which software did he use?

@DanielSmania 3 года назад

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

@mackhomie6 3 года назад

i want this guy on my team after a nuclear holocaust. me and a bunch of mathematicians.

@MoorganHart 3 года назад

Yeah, another well done video. I am left wondering the relevance of the Mandelbrot Set though. I'm not a mathematician, and I've never heard of it before. I'll do a web search, but would have liked to hear about where the equation came from within the video.

@Polarwhisper6 3 года назад

I think you meant: "I am 'A' mathematician"

@christianmathison5892 3 года назад

@@Polarwhisper6 he didnt claim to be an english major

@Sergiuss555 3 года назад

@@christianmathison5892 to be fair there could be girls among those mathematicians.

@warrenchinn4114 3 года назад

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 !

@warrenchinn4114 3 года назад

@@shyamkarthikeya4769 That was my point ... :)

@supteg2.495 3 года назад

@@warrenchinn4114 again a smart man..

@genericusername4206 3 года назад

Warren Chinn true

@bfern053 3 года назад

@@shyamkarthikeya4769 delete this

@DickEnchilada 3 года назад

I learned about this constant (and the equation) when I was taking a System dynamics course 2 years ago. Absolutely loved that course. Stay learning dude!

@jaianupamvarun8722 Год назад

I truly am humbled by the way you present such a complicated topic in such a simple way that even i who isn't a fan of mathematics got interested immediately 😃❤️💕

@S.Ali_Almosawi Год назад

After this video I was able to see John cena

@weo9473 20 дней назад

💀

@TheMsksk 4 года назад

"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!

@SergioEduP 4 года назад

It lowered it for an 18 year old too =P maybe there are even younger people watching, and if there aren't we could share the video to them

@incription 4 года назад

@@SergioEduP 17, beat that

@arvintis2293 4 года назад

InCrIpTiOn 16.

@incription 4 года назад

@@arvintis2293 I think krish beat both of us

@tomifiju 4 года назад

@Krish Kalra yet here I am during meiozis I

@jemert96 2 года назад

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

@futurefacts6909 2 года назад

hahahahaha

@futurefacts6909 2 года назад

is it normal this video gave me goosebumps ?

@londonkoster3888 2 года назад

@@futurefacts6909 yes

@jvm53 2 года назад

yeah, you are special...

@londonkoster3888 2 года назад

@@jvm53 she is

@penguinswithpencils2333 4 месяца назад

I ran across this video about a month into my discrete dynamical systems course. It has been super helpful to have something that gave me some intuition surrounding these patterns before I encountered them formally in class. Sharing it with my professor now :)

@shamsamir1698 Год назад

One of the most beautiful videos on youtube! keep getting back to it every time.

@briancherry8088 4 года назад

8:43 - Boom. Mind blown. We've been missing the 3rd dimension of the Mandelbrot set this whole time.

@mikeciul8599 4 года назад

Actually, I think there might be a 4th dimension, because for some complex values of c, the equation could converge to complex numbers.

@DemonSwrd 4 года назад

now imagine the 4th dimension.

@briancherry8088 4 года назад

@@DemonSwrd - no. The world will explode.

@hammerth1421 4 года назад

@@mikeciul8599 It is the real part of the complex value returned from the complex logistic map. If the result was also complex the Mandelbrot set would be 4D.

@brando3342 4 года назад

@@DemonSwrd We can't imagine that. That's like asking someone to imagine a one dimensional point. Yes, some cosmologists want to say that was what the singularity was at the beginning of the universe, but think about it, it doesn't make sense.

@TehmasKhan 4 года назад

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

@za012345678998765432 4 года назад

I didn't even notice until you pointed it out, thought it was like 9 minutes

@MartinBuzon 4 года назад

@@za012345678998765432 I was going to say 9 too. Damn witchcraft.

@za012345678998765432 4 года назад

@@MartinBuzon Next thing you know Derek comes here and tells us that this equation can explain that as well and it was all planned from the start XDD

@setsugennoao3137 4 года назад

@@za012345678998765432 same

@KillaahMusik 4 года назад

It felt like 4,669 minutes

@matgeezer2094 Год назад

Again, did not expect to be blown away but am utterly. Superb video, bringing quite a 'dry' subject alive.

@harshildobariya6773 11 месяцев назад

One of the most mind-bending concept I have came across. I love your channel, it is one of the best.

@andriypredmyrskyy7791 4 года назад

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.

@Rotem_S 4 года назад

Actually the first physical chaos measured was an engineer using a simple circuit with a transistor and a harmonic input, where he sometimes saw one period, sometimes two, and sometimes all of them

@austinwessels 4 года назад

I was thinking about controls too for most of the video!

@revenevan11 4 года назад

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.

@brocktechnology 4 года назад

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.

@revenevan11 4 года назад

@@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.

@JohnSmith-gs4zv 4 года назад

13:57 "What _really_ *IS* a faucet?" - Vsauce music starts

@impanthering 4 года назад

ok John Smith

@calix451 4 года назад

I miss him

@geekjokes8458 4 года назад

But his video would actually *start* liake that And finish by talking about *UNIVERSALITY*

@DrSpooglemon 4 года назад

"This is water dripping from a faucet. OR is it?!"

@ricardopieper11 4 года назад

I read the first 3 words of your comment in michael's voice before acknowledging the word "vsauce" in it

@nfc14g Год назад

Feels like when you are using exponential equations your inputs are very important and deserve a lot of explaining why you chose it, regardless of real value or best estimate value

@potat8089 Год назад

I remember watching this video when I was about 14 years old and being fascinated by this, but my understanding kinda dropped off when the Mandelbrot Set came into the video (I knew nothing about it). Rewatching this video at age 16, I can really appreciate it so much more, now that I understand it. Thank you for introducing me to the Logistic Map!

@DreamLoud05 4 года назад

THat was definitely one of the shortest 18 minute video I have ever watched on youtube. Very fascinating

@FnaticKiller 4 года назад

Now that is a compliment.

@IRL.johnny 4 года назад

this is frighteningly true... I watch it at 1x while my wife brushed her teeth... how's that possible?

@diabl2master 4 года назад

wtf, I did not realise that was 18 minutes, I was totally enthralled

@pdutube 4 года назад

If you observe a subject watching this video at a specific fraction of the speed of light, you could see it at 18 minutes no matter what the subject's playback speed was.

@liqwiz 4 года назад

I felt Exactly the same. Only by reading your comment I realised "wait... That was almost 20 minutes?"

@user-qx5cn1si1q Год назад

Things like these actually make our world more magical than any science fiction

@glowerworm Год назад

We're living in a simulation and the 4.669 number just happened to be one of the global variable definitions.

@ihatemicrosoftsobadly3188 Год назад

@@glowerworm Dear matrix guys don't use global variables it's bad practice

@glowerworm Год назад

@@ihatemicrosoftsobadly3188 lmao, maybe it's destiny that every programmer, no matter how powerful, will write bad code.

@ihatemicrosoftsobadly3188 Год назад

@@glowerworm so true ... ;)

@justpassingbyy Год назад

@@glowerworm Shoulda been 4.2069 imo

@IIronyy Год назад

Dude I have absolutely no idea of anything I just heard but I still listened all the way through it takes a very talented type of person to intrigue his audience that much.

@rianschoeman559 Год назад

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.

@Prophet_Isaiah 10 месяцев назад

So cool

@ShiftK 3 года назад

**slightly opens kitchen faucet* Me: I'm somewhat of a scientist myself

@bilalthefighter829 3 года назад

lmao

@treewizard4508 3 года назад

Have you written a scientific paper?

@Hwywbwjw 3 года назад

Tree Wizard wat

@ginoyesano5649 3 года назад

Your comment fits your profile picture so well 😂

@Hapasan808 3 года назад

*slightly opens kitchen faucet * Me in a Joker voice: "I'm an agent of chaos."

@sloanehowell6166 3 года назад

“When this baby rotates on the z-axis, you’re gonna see some serious sh*t.” - Dr. Emmett Brown

@davememelandcanada6722 3 года назад

We don't talk about the Doc, since he f**ked up the timeline for 2020.

@chop-daresistance7514 3 года назад

Wow doc.. that's heavy

@chop-daresistance7514 3 года назад

@@davememelandcanada6722 I don't think that was doc.. I think that was biff when he stole the DeLorean

@anasaamir5595 3 года назад

wht is z asix

@Leosayshi 3 года назад

@@anasaamir5595 If I had to guess it’s probably another axis like the y and x axis except it’s used for 3D shapes.

@KM-co5mx Год назад

We need more videos like this! ⭐️

@preranaprasaddeshmukhbe20b34 5 месяцев назад

This is one of the most amazing video I had seen on RU-vid till now

@MrTigershark11 4 года назад

6:37 One of the best plot twist I've seen in my entire life

@snowfloofcathug 4 года назад

Hereizer Oh that pun is wonderful

@madalinspoiala1249 4 года назад

You need to be higher. Great pun

@theshocktart 4 года назад

Such a legendary comment, bravo...bravo!

@justarandomdood 4 года назад

Dad joke levels are through the roof

@NiranjanDixit23 4 года назад

Get out lmao

@bradleyewoodworth 3 года назад

Out of all of the RU-vid channels that I don't understand, this one is my favorite.

@zaphodsbluecar9518 3 года назад

ROTFL - Nice work Brad! :-)

@AzTech71 3 года назад

Lol

@Streamwalker1000 3 года назад

LOL ! I'm with you on that.

@simphiwenxumalo4387 3 года назад

@@Streamwalker1000 LOL me too

@johnmartin9451 3 года назад

I'm sure you understand more than you thought, otherwise you wouldn't be drawn in. It's about patterns and randomness and how the two shall not meet.

@samuellafleur890 20 дней назад

Having just watched your video on the ubiquity of 37, I couldn't help but notice that was the first example you provided when taking about period doubling sequences of any length!

@namakoro_osu Год назад

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

@sidsixpoint7 3 года назад

Jokes on you, this didn't change the way I see the world because I'm dumb.

@HerGatiox 3 года назад

at least you see that. You know that you don't know anything. congrats

@gabeharrison7683 3 года назад

@@HerGatiox a bit condescending

@Zain69z 3 года назад

Lmao

@aaroncruz9181 3 года назад

You see math without numbers

@BenDover-vh9rs 3 года назад

@Majin Buu then how tf does he know that?

@CHLOCHLOLP 3 года назад

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.

@CHLOCHLOLP 3 года назад

@chcpr1 i think its more that no one in power cares to invest in school systems to make them better, but I dont think they are shitty on purpose, just due to neglect. Why would rich government officials care about public schools when are their kids are privately educated anyways, you know?

@Eden894HisBiome 3 года назад

Yeah sadly they don’t teach you anything your not tested for. Unless they a good teacher.

@kaffeetasse9455 3 года назад

One of my teachers actually showed us the mandelbrot set and told us about chaos teory. :D

@chrisbarber7291 3 года назад

Um, they do teach this.

@sirxobsidian408 3 года назад

Unfortunately, this simply isn't true. I'm a high school math teacher, and I've shown this kind of thing to my students on numerous occasions, and the response is pretty much always the same; disinterest. If it's not on a test, they see it as an excuse to take a nap, zone out, or work on other classes' assignments.

@iamlubos Год назад

Great video! It's also a really good subject for a take-home final exam in a scientific computing class I am teaching this semester.

@magic.marmot Год назад

I've been studying emergent behavior since the 80's, when I first read Conway's Game of Life. Back then, it was treated as a nuisance, irrelevant, and annoying. I love watching the break into oscillation as your R-value changes .That's the same behavior as a damped spring, or feedback in an audio system. The transition to chaos between states makes a lot of sense. I love the visualization of the Mandelbrot set, that gave me the perfect starting point to understand it in another dimension. Wonderful.

@veritasium 4 года назад

Feedback from UCLA A/Prof Heather Zinn Brooks: "At first, it seems totally crazy that increasing r would lead to cycles... if it's describing population growth, why would a bigger r cause a drop in some years? In fact, the magic is in the (1-x_n) factor of the equation, which models a carrying capacity. The idea is that populations are typically resource-limited, so growth can only be supported up to a certain point. Once you think about that, it makes sense that huge growth rates could result in "boom and bust" cycles in the population, because the population would grow faster than their resources would support."

@shetty98 4 года назад

1:30 @m in 🇮🇳

@NatePrawdzik 4 года назад

I imagine increasing rabbits also increases wolves, so that probably factors in as well.

@timezone5259 4 года назад

Yes

@gordonrichardson2972 4 года назад

This topic came up when I was studying applied mathematics around 1980: en.wikipedia.org/wiki/Lotka-Volterra_equations

@11quinnjet75 4 года назад

Can this be applied to the expanding universe? because it has a growth rate and if I remember right scientists think that that rate has changed?

@PietchRhum 4 года назад

I feel so dumb! I have a PhD in Ecological Modelling, I have used this equation - and more complex version of it - to model population dynamic multiple time and I didn't knew of this Feigenbaum constant!!! I had teaching on Chaos and none of my professor mentioned it! Well, thanks Veritasium for teaching us new things!

@KarasuInaiga 4 года назад

P. V. I read that as “Executive Meddling”.

@metanumia 4 года назад

@@KarasuInaiga 🤣

@spencerquirk6917 4 года назад

@@KarasuInaiga 🤣🤣🤣

@BrandonRx2 4 года назад

Huh

@ansh6370 4 года назад

Bruh I'm just an eight grader. Tomorrow's my maths test and I'm supposed to learn mensuration and algebra but I'm here trying to figure out what this video even is about after watching it for the 7th time.

@rudyardkipling4569 Год назад

Excellent video. The ubiquitous emergence of the Feigenbaum constant is just disturbingly, weirdly beautiful.

@Khpr666 Год назад

Bro! I love you! Thank you! Your work is increasing the growth rate of knowledge.

@slaughterround643 4 года назад

Veritasium: "Students can have a little chaos, as a treat."

@joshgiesbrecht7060 4 года назад

literally my teaching strategy

@AaronRWilliams97 4 года назад

*little a chaos

@bengardner8639 4 года назад

If you're gonna reference the meme, at least do it right. It's "little a", not "a little".

@marcushendriksen8415 4 года назад

Make them climb a ladder for it, though

@AaronRWilliams97 4 года назад

Ben Gardner *le sigh* He DID say pedants were necessary..

@RPS2443 4 года назад

"The mandelbrot set is numbers that don't blow up" Mind blows up. Seriously the best explanation ever. Then he shows it in 3d. Learned more in 20 minutes than in the last 20 years.

@userMikeforsure1997 4 года назад

I felt that.

@hannesthurnherr7478 4 года назад

so your saying your mind doesnt belong to the mandelbrot set?

@kennyogbogu7777 4 года назад

Now that's funny.

@RPS2443 4 года назад

@@hannesthurnherr7478 Well, rules are rules, so apparently you are right!

@vishalrander9805 Год назад

Very much obliged to watch your videos. Thank you for making the complex to simple .

@lintonatlas8933 Год назад

Outstanding explanation of chaos theory. I especially liked the unifying of the madelbrot set diagram and the doubling diagram, I don't recall seeing that before.

@somethingtojenga 4 года назад

"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.

@djb903 4 года назад

I turned 37 yesterday and I'm glad I've heard of it thanks to Derek

@arvind8302 4 года назад

SomethingToJenga 100%

@binashah3106 4 года назад

well im 7

@spb1179 4 года назад

Bina Shah good keep learning. You might be remembered for something awesome if stuff like this interests you!

@binashah3106 4 года назад

jk im 13

@locotx215 4 года назад

6:41 - "The Plot Twist" figuratively and literally

@aliffikri1888 4 года назад

Noice

@himagnamukherjee9382 4 года назад

pure gold

@carsonmorris127 4 года назад

This whole video is a plot twist

@papa_pt 4 года назад

bravo

@DoktorIgnaz 4 года назад

HOLY

@zx8979 Год назад

Excellent video! A good video to let me know more about chaos after hearing it in class, while my teacher didn't say too much about it.

@VisualJoey Год назад

You definitely did this topic justice in my personal experience! Thank you (…) And this is just one topic where you do justice. I don’t practice maths nor more of the topics you have covered. At least, in a professional or study kind of way that is. However, I have found your explanations to be inspiring and fascinating. You really hit a spot of interest of which I have always had an interest for but never got my head to understand due to the complexity. It’s a gift to be able to watch your videos and get a grasp of understanding. Even though sometimes the grasp barely touches the surface.

@phillipejane8423 4 года назад

RU-vid algorithm - 1st stage - sends to people who are actually interested in math. Less views 2nd stage - sends to related viewers. Less views but still constant. 3 stage - Sends to random people on their feed. Fluctuations in view cycle (no negative views so it shoots up) 4 stage (chaos) - recommends to people like me of all people. Millions of views

@tomas_horn 4 года назад

top comment!!

@norahclarissa6352 4 года назад

This observation is actually clever, considering that the algo is an AI

@manictiger 4 года назад

Recursive view count increases!

@RahulKumar-sy4xg 4 года назад

RU-vid's algorithm decode!

@jordanponton255 4 года назад

Stage 5: people in the Mandelbrot set

@liondeluxe3834 3 года назад

This video made me obsessed. I didn’t sleep last night. This morning I went to my core editor and made a Mandelbrot’s Set visualizer and I watched this video for a second time. I now want to make a logistic map visualizer. Thank you Veritasium.

@aion2177 2 года назад

github link please?

@jamesfield5415 2 года назад

I got obsessed too it’s mesmerising

@NovaWarrior77 2 года назад

please let us know. I for one for sure want to see it.

@goutamboppana961 2 года назад

the beauty come when u keep zooming it

@CrackedCandy 2 года назад

Oh my, my heart is beating faster now, so, where can I see this art?

@DavidMauas Год назад

This is really mind-blowing, I absolutely love it!

@siddiqisah1452 11 месяцев назад

Don't worry I was not got at maths in my teens or 20s, get a quiet room a pen and paper and watch this several times and it will come to you.

@Hgulix62 4 года назад

This is like when you start a new project or new year resolution. Everything is fine and simple at first, then progressively and unexpectedly everything turn to chaos

@eternalexperience2489 4 года назад

Probably the rate of degradation is 4.669 :o

@CuteC3 3 года назад

So basically like when the bass drops, the tempo keeps doubling until it just goes into complete madness.

@Cher007 3 года назад

The 101 of Speedcore and Splittercore 😂

@sethreardon8805 3 года назад

Something tells me that you might have said the smartest thing in these comments. Music is vibration, vibration is periodic. This equation probably can be found in music somewhere...

@TheMaxwellee 3 года назад

I hope a nerdy DJ builds his set this way

@StormEngineer 3 года назад

I almost spit my coffee. Well done.

@RCFrizz 3 года назад

@@StormEngineer Imma go brew some coffee so I can almost spit it!

@nsfa19 Месяц назад

This has got me really interested and fascinated as well. Congrats on such high quality top-notch videos! Thank you very much!

@pudayshankar1036 Год назад

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..

@infinitiv525 4 года назад

I am so glad that some lad just woke up one day and decided: "You know what, I should do some research of dripping faucet."

@TheFredmac 4 года назад

That would be a lad that doesn't get government funding.

@blackdaan 4 года назад

weed is good for some things...

@rtleitao78 4 года назад

You mean, instead of fixing it?

@BenjaminCronce 4 года назад

you mean "woken up by a dripping faucet"?

@variable7833 2 года назад

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

@robologo 2 года назад

Yeah it's very strange... all these formulas that pop up everywhere. I think there's an explanation though.

@pablooo8280 2 года назад

@@robologo have u tried psychedelic drugs? you actually start seeing these everywhere

@mysonandme8424 2 года назад

@@pablooo8280 nobody has because drugs aren't real.

@obiwanjaco 2 года назад

@@pablooo8280 no

@obiwanjaco 2 года назад

@@mysonandme8424 yes

@rainthevaporeon7852 Год назад

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

@mikedavies5551 4 месяца назад

Brilliant especially the final part about different functions. That is new to me. Thanks.

@keving1085 4 года назад

Fastest 18 minutes of my life. I think I actually found what I want to be when I want to grow up. A mathematician

@muttersoehnchen100 4 года назад

Kevin Guanoluisa can’t recommend

@luisfelipe5589 4 года назад

Ha Ha Ha

@manamritsingh969 4 года назад

Do it 👍 Maths is the supreme language of the universe. If you wanna understand the universe, math is the way. I embark on the same path and it's amazing

@kayush01 4 года назад

Manamrit Singh not really, mathematics is an abstract concept and it won’t make you understand the universe. It is more of a tool that you can use to „understand” the universe through physics. I know several brilliant mathematicians who decided to study physics when they understood the difference. Mathematics is not really that interesting when it comes to studying it. It’s the same as learning about black holes in physics, it’s a very brief lecture compared to other stuff that might seem boring like mechanics, kinematics, rigid bodies, aerodynamics etc.

@yourboyskar 4 года назад

What if you don’t want to grow up lolll

@belgianbushrc7934 3 года назад

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

@eletinalex 3 года назад

covid-19= this is control over the rabbit population

@naturelovingfroggy6348 3 года назад

Well said, me too x

@shadowpresident4203 3 года назад

That's probably the ideal situation. If a tutor were to customize a lesson for you specifically, they'd probably aim for a difficulty level you'd find interesting, and a lecture that you could mostly follow. You'd also be very slightly outside your comfort zone, to give you room to "grow into" the lesson. It would also be a bit challenging and would leave you with a few questions to mull over, thereby slightly increasing the chance of watching another video, or of reading a book or article on a similar topic. Your comment would probably be music to the ears of a lot of educators.

@eletinalex 3 года назад

@@shadowpresident4203 thx

@comet1954 3 года назад

I feel your pain! I truly do....

@jfidel3943 Год назад

I love James Gleick's Chaos book. It's such an amazing book and I always learn something new from it.

@rajeswaranparameswaran6611 Год назад

Amazing quality of presentation! Besides being a scientist with msrcellius 'teaching' skills, you are a classic cameraman too! Grateful.

@g0g0duck20 4 года назад

Me: Watches video because I think I'm smart My brain: Hold on there buckaroo

@paratame105 4 года назад

I feel attacked

@AverageAlien 4 года назад

Don't worry we're all retarded here. Welcome to the club.

@Dontlagmebro 4 года назад

Well how do you think (we) get smart?

@trevsanna 4 года назад

LOL....You can actually apply the equation to your comment to see how funny your comment actually is! :)

@rznleagueoflol4545 4 года назад

Trevor Baylis no u cant

@marcushendriksen8415 4 года назад

I'm 27, and I'm glad I didn't have to wait 10 more years to find out about this

@Ptochkaman 4 года назад

Same

@droy333 4 года назад

Numberphile shared this in 2017.

@samuelschonenberger 4 года назад

And I'm 18, and I'm glad I didn't have to wait 19 more years to find out about this

@mustafashafiq3473 4 года назад

i’m 17 haha

@maddie-ub3ze 4 года назад

I’m 17 and glad i didn’t have to wait 20! Hahaha

@keyvanmalaie Год назад

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

@mihalykort84 Год назад

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!

@vincenzkoop43 3 года назад

6:43 most underrated placement of the term ‚plot twist‘

@wedantil 3 года назад

Pun of the day!!!!

@kennethsizer6217 3 года назад

I love you, man!

@Surya-jz6te 3 года назад

german?

@cadosian078 3 года назад

Top 10 anime betrayals

@snowstarsparkle 3 года назад

i don't get it, please explain !

@t-riz7630 4 года назад

Me: cannot do basic calculus *sees title of video* RU-vid just gets me.

@BudEnzo 4 года назад

I taught myself basic calculus from videos on RU-vid. Both Khan Acad and 3blue1brown really helped. I was able to skip Math 251 (Calc 1) at my college and move straight to Calc 2 after a 4-year break between studying BASIC algebra in high school and returning to college.

@tishafeed8085 4 года назад

@@BudEnzo wait what, you studied basic algebra in high school?

@BudEnzo 4 года назад

@@tishafeed8085 I guess lol. My school called it pre-calculus so basically it was algebra+trig.

@tishafeed8085 4 года назад

@@BudEnzo what years/classes? in my highschool (9th-11th year) we did trig+calculus

@tishafeed8085 4 года назад

@gamecube.enthusiast - - i did, but the fundamentals were studied in years 5-9, then it was trigonometry and calculus. Actually, i just realised it depends on what you call 'highschool'

@moumous87 Год назад

After 3 years, watching it again. Love this video!

@NuhDhulMitrain Год назад

I attend a lecture about chaos, first it was dull and now it has become very interesting and fun, also numerically solving equations and getting those pictures

@No-pm4ss 4 года назад

Sometimes, I feel like I can't even comprehend the almost divine beauty of math. You blew my mind a couple of times in this video...

@gickygackers 4 года назад

Anki math is created by humanity

@gickygackers 4 года назад

Therefore not divine bro. Don’t forge to pick up your Quran bro 😖 bless

@Insultthumb 4 года назад

@@gickygackers wtf?

@ryugo7713 4 года назад

Murica Presents huh

@slimal1 4 года назад

@@Insultthumb I think he means "god did it"...or some such rubbish

@avrenna 4 года назад

When the Mandelbrot set rotates: whooaaaahhhhh

@xiaoxiaoxiao686 4 года назад

5erif meme echoes in my head...

@Adam_Bosscoe 4 года назад

Right!?!?!!

@valentinbernard8126 4 года назад

Yeh that was spectacular

@trickytreyperfected1482 4 года назад

"You're not supposed to do that!"

@aurelia8028 4 года назад

I swear to god, my mind was blown away by that! I had only ever seen the Mandelbrot Set as that 2 dimensional boundary thing, so seeing that it was actually a 3D-thing was insane

@Devisidev Год назад

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.

@Elletanvilla Год назад

Thank you so much for this video!!! I can’t understand it fully but my God it still moved me to tears

@farhan132_ 4 года назад

The more I learn, the more I realize I don't really know anything!

@mdestwo 4 года назад

Ah, so you really have been paying attention! That seems to be one of the more important lessons to learn in life. So, here’s to you, me, and everyone else realizing we know less and less each year! 😀

@farhan132_ 4 года назад

@@mdestwo Well said!

@glaucovillasboas8212 4 года назад

That's for sure. I always think I'm smart, but a year later I always remember how stupid and dumb I was, and it keeps repeating

@avikdas4055 4 года назад

Exactly man. But now I'm 100% convinced that I know absolutely nothing.

@Kraflyn 4 года назад

welcome to the club! :D

@ShilpanGPatel 4 года назад

I saw the video title and thought “oh suuuuure this will change my life”, but wow I did not expect to be so taken aback by this. Something so fundamental which I’ve never heard about before!