The Mandelbrot Set 

Michael definately lost the keys to the Vsauce channel

I just wanted to let everybody know that Mandelbrot literally translates to almond bread

In kindergarten: “the numbers, what do they mean?” In highschool: “the letters, what do they mean?”

0:14 DONG? No no, this has always been D!NG.

Only Michael of Vsauce could say, "I also listed off prime numbers for three hours" and follow it immediately with "that was a treat for me ..." and it sound normal

09:41 On Michael's toys.. you never know what's gonna happen **kiss**

The way Michael draws the symbol for infinity is unsettling

8:14 You can't draw ∞ as "oo", it's against the law!

I love how self aware Michael is about his place in meme history.

Because on Michaels toys... You never know what's going to happen *kiss*

The Mandelbrot set terrifies me. A single, small island on an eternal, bottomless sea.

“What’s up DingDongers, my name is Michael, and today we’re going to be listing off the 8 breeds of cats that might be able to learn how to play the banjo” Best ten seconds of my life

I miss the "Hey Vsauce Michael here"

You can't trick me. A new vsauce video was in that small box.

It's amazing that he covered complex numbers, graphing them, iteration, sets, convergence, and divergence in just a 15 and a half min.

Please do a video on The Mandelbruh Set!

Did you just call me a *_Ding Donger_* ??

Micheal: what's up ding dongers Gangster:what's this mufuka doing on our block cu

Vsauce(one of the smartest people in the world) Also him: “what up ding dongers”

My guess for why the box says "IEN": the four pieces are shaped like 's', 'c', 'c', 'e', so it spells "science".

3:29 meme gold

14:27 "This is the only clue I'll give you" *Knocks on the object* So it's a solid object, that narrows it down a bit.

9:36 was an absolutely incredible moment

" It's really beautiful, I really wish it was real" COMPLEX. Take it or leave.

This Michael seems cool. He should start a RU-vid channel!

you can see how michael is slowly losing his mind with each video and its fantastic!

somebody: yeah but i is a letter not a number michael: *fuming* YUSTPITISWERTOGOD

00:34 I think Michael is officially insane

9:44 it’s like he wants to be memed

>buys 4K monitor cos 4K iz future >no 4K footage for years >Vsauce uploads 4K video >internet is not good enough to watch it

7:26 onederful

Whenever I feel sad I always come back and rewatch old Vsauce/Ding dong videos cause Michael always makes me feel wanted

From the Mandelmap website: "No corners were cut and nothing was rushed in the making of this poster; everything was created to the highest level of finish possible." Then there's this with its Main Cardiod

11:12 "I really wish it was real" Yeah, I also wish it was *REAL* , but sadly, it's only *IMAGINARY* .

I really like your videos. Your love for knowledge and your personality when explaining the subject is awesome.

1:30 Doesn’t every island technically have an infinite coastline because of the coastline paradox.

Hey Michael, "cardioid" is misspelled on the map! Might wanna fix that real quick before shipping em' out

WHADDUP DING DONGERS

3:29 the funniest thing Michael has ever done imo

cause on michael's tooooys... you never know what's gonna happen **smooch**

DONG is the new vsause and vsauce is just a mindfield exclusive channel

at 10:20 you can see a mistake on the map it says, "Main Cardiod," but it should say, "Main Cardioid" uh oh! that's no bueno!

I'm always impressed and learn everytime something new. Love you guys

13:24 - 13:31 Michael's true self shows, one day he will come back.

Please, say, hey vsauce, Micheal here I miss you😭😭

I love Michael and I love Vsauce but after reading the comments, seeing Bill's map, and reading his explanations of the gridlines and just the sheer amount of effort and forethought that went into his map, I'm off to buy his version. It is a thing of beauty and a work of art! I feel bad for Bill since Michael and team did not give him credit but at least watching this video lead me to finding something worth purchasing.

thank you. I love making art with fractals and get how it works but this really explains it. I love what you are doing. what a great idea!

On past occasions here and there - I tried to find a place where the Mandelbrot Set (or at least the concept behind it's geometry) was explained in a way that I could understand. This guy here (Michael) finally did just that in this video - and in a way that was both clear and concise. He explains the odd "equal" sign: that it means the relationship between what is on either side of that 'equal sign' is based on a repeating function which loops a value back -based on a given starting value. And he gives a good demonstration of how that works (along with giving a quick example of complex numbers). People have SAID it was fairly simple - but this is the FIRST TIME - it was ever explained in a way that I found understandable! So, Thank You, Michael for doing a nice job of that in this video!

When will you do a face reveal?

9:45 the suss level is high and this is y i love this *kiss back*

Lmao why’s he calling it D.O.N.G, this channel is and always has been called D!NG

Michael you sir are one of my heroes. You have just made my imaginary dead or alive tea party! I love your sense of humour but more what you do for charity is inspiring! Keep it up!

9:00 Mr. Stevens what did we learn about using parenthesis when squaring negative numbers?

1:04 the Stanford Prison Experiment?! Exciting?! wow what a response Michael...

Haha that kiss! 😂😂 your humor is right up my alley bruh! Keep kickin’

3:08 that lick tho

Remember when Vsauce(1) made videos that were not premium content

Hey Michael, Vsauce here

3:24 Michael: Someone probably said "Yeah but "i" is a letter, not a number." Me: Hey, that's me!

Love that you generously gave us two free videos without at all acknowledging how all of your content used to be free

“I don’t care. I sit the way I want.” -Michael Stevens 2018 You damn rebel.

Hello fellow Ding Dongers in the comment section.

10:40 Michael is so cute here

I seriously find more comedy in this than any other channel on RU-vid

I wish you'd just continue uploading on Vsauce

Is there a typo on the map? It says "Cardiod" instead of "Cardioid".

But which cat can play the banjo.

Michael you're actually living your best life

Ding dongers? Oh no I'm scared for my life

I will delete this comment if this gets mentioned in the video but "Mandelbrot" is "almond bread" in German.

Soooo awesome! Thank you!!

The Mandelbrot set is the set of complex numbers c for which the function f (z) = z2 + c does not diverge when iterated from z = 0, i.e., for which the sequence f (0), f(f(0)), etc., remains bounded in absolute value. Its definition is credited to Adrien Douady who named it in tribute to the mathematician Benoit Mandelbrot. The set is connected to a Julia set, and related Julia sets produce similarly complex fractal shapes. Mandelbrot set images may be created by sampling the complex numbers and testing, for each sample point c, whether the sequence f (0), f(f(0)),... goes to infinity (in practice - whether it leaves some predetermined bounded neighborhood of 0 after a predetermined number of iterations). Treating the real and imaginary parts of c as image coordinates on the complex plane, pixels may then be coloured according to how soon the sequence f (0), f(f(0)),... crosses an arbitrarily chosen threshold, with a special color (usually black) used for the values of c for which the sequence has not crossed the threshold after the predetermined number of iterations (this is necessary to clearly distinguish the Mandelbrot set image from the image of its complement). If c is held constant and the initial value of z-denoted by z0 is variable instead, one obtains the corresponding Julia set for each point c in the parameter space of the simple function. Images of the Mandelbrot set exhibit an elaborate and infinitely complicated boundary that reveals progressively ever-finer recursive detail at increasing magnifications. The "style" of this repeating detail depends on the region of the set being examined. The set's boundary also incorporates smaller versions of the main shape, so the fractal property of self-similarity applies to the entire set, and not just to its parts. The Mandelbrot set has become popular outside mathematics both for its aesthetic appeal and as an example of a complex structure arising from the application of simple rules. It is one of the best-known examples of mathematical visualization and mathematical beauty.

3:29 My man Michael just pulled a Pewdiepie

Eye witnessing Micheal's transformation into Kratos.

I'm not sure if this will be seen, but thanks for the closing words, I really needed them

3:39 *confused screaming

1:55 when Michael suddenly gets possessed by Jake.

Isn't it cardioid instead of Cardiod?

I’m currently watching this video on Benoit Mandelbrot’s birthday!

Vsuace can make anything Complex into something any"thing" and anyone can do

love this channel because Michael actually posts frequently, I love Vsauce and I understand the perfectionism there, its deserved however I like these videos and its great to be able to get more.

15:07 brought stinging tears to my eyes. I'm leaving this shortcut to it here so I may listen to it over and over. I'm absolutely betting it could possibly save a life, likely mine. I love you too Michael, thanks for saying you're glad I'm here I honestly needed that.

Thanks for breaking this down like this.

I love you Michael, really.

Come on Dong guys, especially michael, you have to ackowledge bill tavis!!!

I just received one by Bill Tavis. I'm from Spain. Everything in the package was perfect. Great purchase.

I have watched several explanations of the Mandelbrot set. I was skeptical about this at first because of the manic intro about cats etc. However, this explanation is by far the easiest to understand. Good job❗️😊👍

I grew up watching vsauce and the music u used in those videos gives an intense nostalgia trip

*Psst* _I think we're owed an explanation on the striking similarities between this misspelled nonsense and Bill Tavis' version_

I wish Michael could understand that all of his content is great. There is no need to feel as if one video is unworthy. Just because you have an awesome show in Mind field doesn't mean that every video has to hold some answer to the universe (which most of them do). We love you Michael, just be yourself.

Omg Michael your humour brings me visceral happiness

You're extremely funny Sir! I love the Mandelbrot set. After watching this video, I love it even more!

He is the pewdiepie of science channels

But that doesn't say cardioid. It says cardiod.

Tbh i like these dong videos more than the original vsauce ones, I like that all the topics are more related and it creates just a way better understanding of what you are talking about.

I used your Prime Number video as a "Pomodoro" timer back when you first released it... still haunts me to this day. Lolol ❤️

Hey VSauce. You should really give the original creator, Bill Tavis, a % of those poster sales.

Basically: Vsauce = the paid content channel (moving forward). DONG = the free stuff.

Happy birthday to the mandelbrot guy

did he just said ding dongers...???