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

[@AustenAlexander]

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

[@nickreed7277]

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

[@Matt_10203]

@@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]

Bro I dont even know what algebra means

[@JoeyLovesTrains]

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

[@luppa79]

Verisatrium :)

[@ColorwaveCraftsCo]

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

[@erteple2647]

looks like a deformed pringle

[@benhsuan4817]

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]

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

[@bestawdomx6835]

@@erteple2647 there is infinite?

[@steveskeletonne-7394]

kzbin.info/www/bejne/b4aTiYmaq7aqd6s This is essentially just a bunch of 3D fractals.

[@tanvisharma6903]

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]

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

[@ashfujiyama]

this is such an underrated joke

[@caturlifelive]

up

[@gingaming_gg]

Pretty much 😂😂😂

[@depressedguy9467]

Go back

[@zanityedpo1398]

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]

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

[@dmajorvgm8735]

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]

@@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.

[@EhsaanTV-j4l]

bro you got a new twin

[@DanielSmania]

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

[@mackhomie6]

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

[@MoorganHart]

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]

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

[@christianmathison5892]

@@Polarwhisper6 he didnt claim to be an english major

[@Sergiuss555]

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

[@youmaybebusy]

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

[@DrIridium]

haha same

[@scurvofpcp]

I know, right

[@IRuinEvrything]

relatable

[@smoothe14]

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]

mandelbulbs are gunna blow you away bro

[@warrenchinn4114]

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]

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

[@supteg2.495]

@@warrenchinn4114 again a smart man..

[@genericusername4206]

Warren Chinn true

[@bfern053]

@@shyamkarthikeya4769 delete this

[@momchilandonov]

But this formula can't be applied to many things! Bacteria and humans are good example of that! Rabbits are not a good example as they simply die a lot... You don't even need some madeup formula to explain the populations interaction in biology. More rabbits mean more food for eagles ;). Lets say the formula normally works. Well if you reduce the death rate of rabbits by placing them on another (safer from humans and eagles) planet the formula wouldn't work for a very long time...Also sudden increase in rabbits population would mean that they don't have food and die from starvation but again this is preventable and generally there are tons of changing factors involved.

[@joekelley5121]

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]

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]

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]

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

[@va941]

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

[@piercelane7757]

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.

[@feynstein1004]

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

[@unathimatu]

it was a bifurcation

[@Binyamin.Tsadik]

@@unathimatu lol, perfect response dude!

[@BasiC7786]

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

[@cezarcatalin1406]

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]

_mind blow_

[@entropy_7827]

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

[@FunTheMentalist]

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

[@kumarsaieshrane9692]

😂😂😂😂

[@masterpsk]

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

[@gangsta6730]

I was like "hol up-"

[@eusebiorozco]

Hahahahaha

[@TheMsksk]

"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]

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]

@@SergioEduP 17, beat that

[@arvintis2293]

InCrIpTiOn 16.

[@incription]

@@arvintis2293 I think krish beat both of us

[@tomifiju]

@Krish Kalra yet here I am during meiozis I

[@maegodragon]

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]

You a rabbit by any chance

[@hugojj101]

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

[@veritasium]

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."

[@shettySJ]

1:30 @m in 🇮🇳

[@NatePrawdzik]

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

[@timezone5259]

Yes

[@gordonrichardson2972]

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

[@11quinnjet75]

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?

[@andriypredmyrskyy7791]

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]

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]

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

[@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.

[@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.

[@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.

[@DreamLoud05]

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

[@FnaticKiller]

Now that is a compliment.

[@IRL.johnny]

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

[@diabl2master]

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

[@pdutube]

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]

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

[@samuellafleur890]

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!

[@BAgodmode]

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

[@jingalls9142]

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

[@shadeop6773]

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

[@asparagii]

yeah that was awesome

[@carriersignal]

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]

Its now my wallpaper!!! That image its insane

[@roshnirana2098]

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

[@AngelOrtiz-wt7xt]

Roshni Rana aqq msm

[@zperdek]

Chaos is magic.

[@PavR376]

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

[@ГенадийПопов-ч7б]

My apologies! if you are not interested in my offer I am from Russia .I live in Siberia looking for a sponsor (investor), please send this information to interested parties and companies..Thank you for reading with respect Popov Gennady. Today, for all progressive, caring people who care about the fate of the planet, the fate of people, the fate of humanity! Today, it is unequivocally and irrevocably clear that warming is the main threat to humanity. It is extremely important to pay attention to projects that can change the situation on a global scale. to stop further warming. The main supplier of gases that provoke warming is a thermal power plant, which burns coal, gas, oil,...and the atom, too!. Exactly my invention… Still I ask all people who are not indifferent to the problem! convey this message to interested parties and companies...

[@jemert96]

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

[@futurefacts6909]

hahahahaha

[@futurefacts6909]

is it normal this video gave me goosebumps ?

[@londonkoster3888]

@@futurefacts6909 yes

[@jvm53]

yeah, you are special...

[@londonkoster3888]

@@jvm53 she is

[@falcxne]

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]

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 :-)?

[@simrans3675]

@@DHRUVSHINDE-tw5uy Religion is man made, faith/spirituality is a different conversation and tough to crack using math or so I think :-)

[@stephenwest6738]

Sync

[@Chord_]

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

[@maumau9466]

Lmao😂😂😂

[@norpriest521]

@@maumau9466 What that means

[@starryepidemic2532]

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

[@koborkutya7338]

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

[@MrSleepyweezul]

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

[@brucefoote540]

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

[@ingridfong-daley5899]

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

[@3orM00Rrecharacters]

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

[@ingridfong-daley5899]

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

[@HiManLOL]

people out there proving existance of god with Mandelbrot fractal

[@convolutionality]

its so pretty my inspiration too

[@garfieldturismo]

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

[@cfneal1459]

Explain? Please.

[@doctorquantum3364]

@@cfneal1459 r/woosh

[@jinx5349]

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

[@rohangaikwad255]

Hahaha

[@maxlank539]

I'm dead 😂😂😂😂

[@Peace2051]

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

[@bradleyewoodworth]

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

[@zaphodsbluecar9518]

ROTFL - Nice work Brad! :-)

[@AzTech71]

Lol

[@Streamwalker1000]

LOL ! I'm with you on that.

[@simphiwenxumalo4387]

@@Streamwalker1000 LOL me too

[@johnmartin9451]

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.

[@blobishlybelfer2717]

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

[@K3zz21]

"when a water will drop" a SINGLE water

[@who-ow5ix]

😂😂

[@plaverbach]

@@K3zz21 When the water would drop?

[@zacharyhall7466]

Chaos theory?

[@haydenbellis3047]

.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

[@edstervedster]

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

[@elee9056]

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

[@carloshogar2]

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

[@airpolygon2714]

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

[@rianby64]

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

[@Cloud7050]

Crowdsourceeee

[@BanditMatt]

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

[@liondeluxe3834]

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]

github link please?

[@jamesfield5415]

I got obsessed too it’s mesmerising

[@NovaWarrior77]

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

[@goutamboppana961]

the beauty come when u keep zooming it

[@CrackedCandy]

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

[@ShiftK]

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

[@bilalthefighter829]

lmao

[@treewizard4508]

Have you written a scientific paper?

[@Hwywbwjw]

Tree Wizard wat

[@ginoyesano5649]

Your comment fits your profile picture so well 😂

[@Hapasan808]

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

[@MrTigershark11]

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

[@snowfloofcathug]

Hereizer Oh that pun is wonderful

[@madalinspoiala1249]

You need to be higher. Great pun

[@theshocktart]

Such a legendary comment, bravo...bravo!

[@justarandomdood]

Dad joke levels are through the roof

[@NiranjanDixit23]

Get out lmao

[@SriRam-se3cu]

When you tilted the graph it made My spine chill , amazing 👏

[@RPS2443]

"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]

I felt that.

[@hannesthurnherr7478]

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

[@shosanboggs]

Now that's funny.

[@RPS2443]

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

[@ВоронМаусы]

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

[@glowerworm]

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

[@eepydragonloaf]

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

[@glowerworm]

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

[@eepydragonloaf]

@@glowerworm so true ... ;)

[@justpassingbyy]

@@glowerworm Shoulda been 4.2069 imo

[@TehmasKhan]

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

[@Darth_Pro_x]

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

[@MartinBuzon]

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

[@Darth_Pro_x]

@@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]

@@Darth_Pro_x same

[@KillaahMusik]

It felt like 4,669 minutes

[@madeeb04]

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

[@veenmikki27]

The point of it is that chaos can’t be modeled but that it comes from that which can be modeled

[@briancherry8088]

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

[@mikeciul8599]

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

[@NightBeyondVeil]

now imagine the 4th dimension.

[@briancherry8088]

@@NightBeyondVeil - no. The world will explode.

[@hammerth1421]

​@@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]

@@NightBeyondVeil 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.

[@CHLOCHLOLP]

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]

@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?

[@Edenmm]

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

[@kaffeetasse9455]

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

[@chrisbarber7291]

Um, they do teach this.

[@sirxobsidian408]

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.

[@attrapehareng]

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]

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

[@metanumia]

@@KarasuInaiga 🤣

[@spencerquirk6917]

@@KarasuInaiga 🤣🤣🤣

[@BrandonRx2]

Huh

[@ansh6370]

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.

[@Sagitarria]

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.

[@ShilpanGPatel]

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!

[@ayaipeeoiiu8151]

Shilpan Patel so you should subscribe to numberphile

[@JohnSmith-gs4zv]

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

[@impanthering]

ok John Smith

[@calix451]

I miss him

[@geekjokes8458]

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

[@DrSpooglemon]

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

[@ricardopieper11]

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

[@keving1085]

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

[@luisfelipe5589]

Ha Ha Ha

[@manamritsingh969]

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]

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]

What if you don’t want to grow up lolll

[@Professor_Utonium_]

Don't let other people ever dissuade you from doing something you find passion for.

[@jeff_tj]

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

[@jawadfarrukh6736]

Do you know which software did he use?

[@Hgulix62]

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]

Probably the rate of degradation is 4.669 :o

[@CuteC3]

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

[@Cher007]

The 101 of Speedcore and Splittercore 😂

[@sethreardon8805]

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]

I hope a nerdy DJ builds his set this way

[@StormEngineer]

I almost spit my coffee. Well done.

[@RCFrizz]

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

[@hidjedewitje]

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!

[@DataJYdocs]

ie: the Lorenz Attractor.

[@albertofoti4152]

Yep, I'm here because I'm studying for an exam ahah Non-linear Control and Aerospace applications

[@GdeJ]

Here's another: Chua's circuit

[@albertofoti4152]

@@GdeJ I am from Politecnico of Turin in Italy and we had the pleasure of having a lecture directly from Professor Chua. I think the Lorenz Attractor and the Chua Circuit are the most thought in control engineering degrees. Maybe talking about non linear systems behaviors we also have systems having limit cycles in the phase portrait, for example the Van Der Pol Oscillator

[@GdeJ]

@@albertofoti4152 I'm from Federico II University! I just had an exam on non linear dynamics and control. Other than Van Der Pol oscillator, our professor mentioned also other relaxation-excitation oscillators, such as Fitzhugh-Nagumo and Hindmarsh-Rose models of a neuron.

[@jaianupamvarun8722]

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 😃❤️💕

[@infinitiv525]

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]

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

[@blackdaan]

weed is good for some things...

[@rtleitao78]

You mean, instead of fixing it?

[@BenjaminCronce]

you mean "woken up by a dripping faucet"?

[@g0g0duck20]

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

[@paratame105]

I feel attacked

[@AverageAlien]

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

[@Dontlagmebro]

Well how do you think (we) get smart?

[@trevsanna]

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

[@rznleagueoflol4545]

Trevor Baylis no u cant

[@vincenzkoop43]

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

[@wedantil]

Pun of the day!!!!

[@kennethsizer6217]

I love you, man!

[@Surya-jz6te]

german?

[@cadosian078]

Top 10 anime betrayals

[@snowstarsparkle]

i don't get it, please explain !

[@magic.marmot]

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.

[@No-pm4ss]

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]

Anki math is created by humanity

[@gickygackers]

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

[@Insultthumb]

@@gickygackers wtf?

[@ryugo7713]

Murica Presents huh

[@slimal1]

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

[@avrenna]

When the Mandelbrot set rotates: whooaaaahhhhh

[@xiaoxiaoxiao686]

5erif meme echoes in my head...

[@Adam_Bosscoe]

Right!?!?!!

[@valentinbernard8126]

Yeh that was spectacular

[@trickytreyperfected1482]

"You're not supposed to do that!"

[@aurelia8028]

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

[@belgianbushrc7934]

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

[@eletinalex]

covid-19= this is control over the rabbit population

[@naturelovingfroggy6348]

Well said, me too x

[@shadowpresident4203]

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]

@@shadowpresident4203 thx

[@comet1954]

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

[@mehamrdio6173]

Thanks!

[@disturb3df4n]

I love how genuinely excited he is about the topics he covers.

[@dhrumildave4221]

yup

[@-lorentzen5925]

True. He really deserve it for all this dedication and interrest into every movie.

[@t-riz7630]

Me: cannot do basic calculus *sees title of video* KZbin just gets me.

[@BudEnzo]

I taught myself basic calculus from videos on KZbin. 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]

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

[@BudEnzo]

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

[@tishafeed8085]

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

[@tishafeed8085]

@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'

[@phillipejane8423]

KZbin 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]

top comment!!

[@norahclarissa6352]

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

[@manictiger]

Recursive view count increases!

[@RahulKumar-sy4xg]

KZbin's algorithm decode!

[@jordanponton255]

Stage 5: people in the Mandelbrot set

[@ainzulgone492]

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

[@Mr_Noob-jp8nv]

Oh yeah, at 6:12

[@anmolkessani4872]

@@Mr_Noob-jp8nv you got 37 likes rn

[@shafsteryellow]

Pissing me off

[@rushatyadav9135]

He also says he's 37 years old At 17:02

[@innalagonska8323]

First time on the synchronicity ride? 😂This 🎢 will only get wilder with time.

[@sk8ersteve]

I used to notice my sink doing this when I was a small child and always wondered what the heck was going on. This video just solved a 15 year old mystery for me. Thank you!

[@aghalar_]

Yeah, but did it actually ... ?🧐

[@locotx215]

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

[@aliffikri1888]

Noice

[@himagnamukherjee9382]

pure gold

[@carsonmorris127]

This whole video is a plot twist

[@papa_pt]

bravo

[@DoktorIgnaz]

HOLY

[@variable7833]

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

[@robologo]

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

[@pablooo8280]

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

[@mysonandme8424]

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

[@obiwanjaco]

@@pablooo8280 no

[@obiwanjaco]

@@mysonandme8424 yes

[@preranaprasaddeshmukhbe20b34]

This is one of the most amazing video I had seen on KZbin till now

[@slaughterround643]

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

[@joshgiesbrecht7060]

literally my teaching strategy

[@AaronRWilliams97]

*little a chaos

[@bengardner8639]

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

[@marcushendriksen8415]

Make them climb a ladder for it, though

[@AaronRWilliams97]

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

[@sloanehowell6166]

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

[@davememelandcanada6722]

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

[@chop-daresistance7514]

Wow doc.. that's heavy

[@chop-daresistance7514]

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

[@anasaamir5595]

wht is z asix

[@Leosayshi]

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

[@Jellyfishhie]

Dude, I'm halfway reading James Gleick's Chaos at the moment. The timing of your video's release is just perfect.

[@VigneshMukund]

Oh, me too.

[@druid_zephyrus]

All praise The Almighty Algorithm! It's the most omnipresent entity! It hears all. It sees all! and It recommends on your behalf. 001100 010010 011110 100001 101101 110011

[@MrDeadlySmile]

I'm curious. May I ask what that is about?

[@DrRiq]

Ayy got it on my shelf; I think I'll read it again

[@ckhalifa_]

If you're looking for a good introductory text on the topic I'd highly recommend Exploring Chaos by Nina Hall and if you know what a Jacobian is and want to really get jiggy wit it then I'd suggest Strogatz.

[@secahtah]

I got chills watching this. Math is beautiful. Thank you for making this video.

[@zakirorrahman9007]

I did not even realise how quickly 18mins passed by. Love you vertasium I want to grow up and do research and share on KZbin just like you . You and Physics Girl are my favourite youtubers

[@seanehle8323]

If you're not aware of PBS Space Time, give them a watch, too. If that's too heavy, check out Isaac Arthur. If you're more into physical experiments, Applied Science or Practical Engineering are great channels. Of course, Numberphile, Sixty Symbols, Periodic Videos, and the rest of Brady Haran's channels are all good, too.

[@terryhalsteadgamer]

Nice choices my friend! Hopefully you already know the channels Smartereveryday and SteveMould. If you like Derek then you'll enjoy these guys too I hope.

[@orbojunglist]

Ikr? Almost at the end of the video, I had to scroll up and check you weren't joking, that felt like about 5 minutes...

[@venominblx9333]

Like 9 minutes in and it feels like 2 hours lol

[@owenchen9069]

Apple 2 never give up!! Study hard in school and you will do great things

[@thereal7118]

This video taught me how hard is it to slightly open a tap...

[@egg250]

lmao

[@reibian]

This video certainly “open slightly” very well.

[@lc7ineo]

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

[@jakewatson1160]

I was interested in it but i will always hate math cuz ths made me fall asleep lol

[@panpsalt6757]

I understood more than I want, but still less

[@thechappist]

Yup! Make me want to go learn some math!

[@thechappist]

I had to write some things down to look up definitions! But interesting

[@unbiasedhuman1659]

Fibonacci equation.

[@Keatwonobe]

I watch this every single time I think about this concept. To be honest, one of the best decisions ever to beat this into my head. thank you for making this.

[@gwyn.]

14:00 I played with this when I was younger and was fascinated to hear the different rhythms it makes. And here I am a decade later learning about it on youtube.

[@the_venomous_viper1234]

You may have broken my amount of mind-blows in one video - the z-axis of the Mandelbrot set? The chaos of Bifurcation? The bifurcation constant? The practical applications? Incredible!!

[@PaulusCunctator]

One thing he didn't mention...there's a second Feigenbaum constant. Not just the length of the tine with its subtine 4.669, but the width of the subtine 2.502

[@akshatshah3717]

I barely understand this at 15 years old but I have a feeling I'll grow into it

[@sameasnow]

@@akshatshah3717 maybe it will grow into you...

[@imaclock8144]

that 3D fractal diagram of the mandelbrot set expanded into its bifurcation expressing form in space, I've seen it before this video, and almost comprehended its nature, but now i see it clearly. and it's so beautiful. that is the single most beautiful object that mathematics has given us.

[@imaclock8144]

i want to give it a more poetic title that does it justice. im thinking "The Mandelbaum Chaos Flower".

[@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.

[@djb903]

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

[@arvind8302]

SomethingToJenga 100%

[@binashah3106]

well im 7

[@spb1179]

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

[@binashah3106]

jk im 13

[@harshildobariya6773]

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

[@The_Tormented_One]

Me: That was fascinating and mind blowing. Me again: What did I understand from this video is that after rabbit, everything was chaotic.

[@jacquesalphonso3636]

Raw...bit ?

[@40watt53]

Joke?

[@ironchump1501]

so thats what "going down the rabbit hole" means. Descend into chaos

[@mysonandme8424]

@@ironchump1501 no, dude, no, it doesn't. so...there, take that.

[@scott-hr3hd]

The battle between order and chaos continues.

[@farhan132_]

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

[@mdestwo]

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_]

@@mdestwo Well said!

[@glaucovillasboas8212]

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]

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

[@Kraflyn]

welcome to the club! :D

[@marcushendriksen8415]

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

[@Ptochkaman]

Same

[@droy333]

Numberphile shared this in 2017.

[@samuelschonenberger]

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

[@mustafashafiq3473]

i’m 17 haha

[@maddie-ub3ze]

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

[@jdaviqwerty]

In about 1980 I was a Physicist working for the Navy when I heard about the Mandelbrot set. Our screen only had 3 colors. I programmed the set and made it zoomable. Such Fun

[@RogerMillerInVA]

You’ve re-kindled the magic! I read “Chaos” thirty years ago. It changed the way I see the world / time / history / physics. Please keep following this path ... you are blowing my 63 y.o. Mind! Thank you!

[@nabeelahmed4862]

@@arnietapp423 lol what

[@nabeelahmed4862]

@@arnietapp423 Ohhh, I see. Thank you for explaining.

[@nabeelahmed4862]

@@arnietapp423 No, Sorry.

[@ностромов]

Nobody is. :P:D

[@SpotonEd]

kzbin.info/www/bejne/b4HZo2Cwa7R-ndk

[@Max_Jacoby]

- What is the answer to the Ultimate Question of Life, the Universe, and Everything? - 4.669

[@Jcornman24]

Nice

[@mmmmmark9751]

It's 42......of course we really don't know what the question is.....(ps. it is 6x9.....which is why it's all fuk dup)....thanks Douglas

[@contessa420]

Nice reference

[@Binyamin.Tsadik]

It's 3 Pi /2

[@RagavPR]

@@Binyamin.Tsadik 1.5xπ

[@sterlinggrinnell]

I got about 6 sentences in and remembered why I failed math.

[@ModernCults]

Exactly what I was thinking hahaha

[@IIronyy]

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.

[@jaichbinachtzehn1]

When i had numerical maths in my University, there was a alot of chaotic stuff we came along and philosophised with our Professor about. Was one of the best classes I ever had

[@Simpson17866]

@earthly firefly5 Amen :)

[@tacitus3591]

Math professors are a lot more mystical than people give them credit for. When I took Calc II in college, I went to my prof and talked about the weirdness of infinity. I don't remember exactly what I said, but he got the funniest look in his eyes and said something like" in many ways, that is the great mystery behind all reality." Then I realized that if you spend your whole life studying math, it must really change your perspective on everything. Peering down into an endless sea of perfectly tuned complexity that most people never think about, and wondering why it's there or where it comes from...sheesh.

[@allanthompson9695]

This made a lot more sense than I thought it would when I first watched it. Eye-opening. I agree, it's beautiful.

[@AshleyMathClass]

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.

[@artdonovandesign]

Yes! Math was so very dry in school- as if it was intentionally designed to be so. This presentation would have made math so more interesting had it been included in the curriculum.

[@xXBenutzer235Xx]

Sad part is, you'd still get the usual "What will we ever need this for?!" in probably 95% of classes.

[@AshleyMathClass]

@@xXBenutzer235Xx yes…I taught HS for 10 years and got asked that question all the time.

[@arminislam6805]

Mathematics is pretty cool tbh- it's just the educational institutes and some dumbass tchrs who made it seem not-so-cool-thing...

[@ramaraksha01]

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

[@NatQuack]

I LOVE this video and only now realised it was uploaded on my birthday :D

[@nonamenofamily405]

This is the most significant video by Veritasium. A strong connection between the logistic map, chaos and fractals. Many deep implications. Beautiful!

[@roslinked]

What are the deep implications? I'm genuinely curious what you have to say.

[@Jessicalc941]

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

[@waterproof4403]

haha same

[@physcedelicanvs]

u nailed it better.i only undestand 0.00001 percent and felt like im the descendant of euklides

[@jerrythemagichamster8586]

The good part is that 5% of the universe is seeable matter sooo.. you understand now about .0025% of the universe.

[@TheBrickagon]

I swear, seeing memes and reading comments make me feel that we all live the same life :))))

[@waterproof4403]

@@TheBrickagon haha some what comforting

[@karldavis7392]

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.

[@lizard7120]

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!

[@gamekyuubi42069]

I've watched this video at least every month since you've released it I just cannot stop it is so incredibly interesting

[@kaylalyons4461]

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

[@GarmagaramAnday]

Chaos is a ladder

[@nerd9347.]

L.O.L, same.

[@direwolf27]

@@GarmagaramAnday Peter baleish

[@ciscoar2625]

Nice lol

[@stevorobo692]

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

[@TheGrandBagel]

13:56 What really is a faucet? Hey, VSauce! Michael here

[@pi17]

Somehow this relation never ceases to intrigue me

[@o_o............]

I actually didn't know what a faucet is...

[@manoskalozimis674]

Dear Veritasium, I ended up on your video after a huge after-midnight procrastination loop (could be chaos theory related, haha) but after I watched the whole video I was stunned. Thank you so much for making this! It really inspired me and reignited my passion for math, strangely enough I am not exaggerating... Thank you again, subscribed, much love from Univrsity of Crete!

[@shishirmaharana4022]

Me too! Is there a thing with vsauce and veritasium videos appearing on recommended when we are procrastinating?

[@potat8089]

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!

[@TheJohnblyth]

Yes, you’ve done a good thing here, for me at least: this is one of the most beautiful things I’ve ever encountered. Wow. Thanks, Derek!

[@RedGallardo]

Try the patterns in music, it might work ;)

[@midoctor]

@@RedGallardo Go I Ching etc. Yet only 30000 days to spend...

[@camjo_io]

3:27 AM Me: *hunched over the sink* My mom: why are you STILL up? Me: SHHH! I’VE ALMOST GOT A CHAOTIC SYSTEM!

[@hareecionelson5875]

now tell me, are you experimenting with a dripping tap, or the still beating hearts of rabbits.

[@ChristiansPrayingTogether]

That's so funny !

[@josecoronadonieto6911]

@@hareecionelson5875 both at the same time sounds like the only logical response

[@lordfelidae4505]

@@hareecionelson5875 mouse livers.

[@hareecionelson5875]

@@lordfelidae4505 I'm afraid it's an r/woosh on my end, don't know nothing about no mouse livers

[@gregvondare]

Visualizing the Mandelbrot Set in the Z axis: phenomenal! That was a real eye-opener. Stunning graphics. Thanks.

You're so right. We're almost exclusively taught things in two dimensions. We live in a three dimensional (well, four actually, but that's another discussion) world.

[@cheesecakelasagna]

Imagine what the Mandelbrot Set would look like in 4D and so on!

[@Stormy4ya]

@@cheesecakelasagna The 4th is time. So you see it in 4d all the time. You need something that´s actually happening for 4 d. A Graphic doesn´t happen. It´s if you remove the 4th D to understand it better.

[@italkmerida8254]

especially when you know that the axis also shows the chakras : )

[@schroedingerscat3099]

@@italkmerida8254 What do you mean by that, that the axis also show the chakras? Genuine question, I've never heard of that before

[@KM-co5mx]

We need more videos like this! ⭐️