The Mandelbrot Set

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  • Опубліковано 13 тра 2024
  • I will send my brain food right to your door: www.curiositybox.com
    / tweetsauce
    / electricpants
    Vsauce PO Box: PO Box 33168
    L.A. CA 90033
    **Click "SHOW MORE" For Links**
    Mandelbrot Zoom
    • Video
    **CREDITS**
    Hosted by
    Michael Stevens
    Edited by
    Jack Merline
    VFX by
    Eric Langlay
    ( / ericlanglay )
    Music by Jake Chudnow
    ( / jakechudnow )
    and Audio Network
    (www.audionetwork.com)
    **VSAUCE LINKS**
    Vsauce1: / vsauce1
    Vsauce2: / vsauce2
    Vsauce3: / vsauce3
  • Розваги

КОМЕНТАРІ • 4,5 тис.

  • @passdoutcouchpotatos
    @passdoutcouchpotatos 5 років тому +9289

    Michael definately lost the keys to the Vsauce channel

    • @TehPobo
      @TehPobo 5 років тому +179

      He will return one day 😔

    • @ICECREAMan2991
      @ICECREAMan2991 5 років тому +111

      Brace Pobo I don’t believe in god but I’m still gonna pray for him to return to vsauce

    • @dickjohnson4447
      @dickjohnson4447 5 років тому +74

      Vsauce is for the series Mind Field now

    • @JorgetePanete
      @JorgetePanete 5 років тому +35

      definitely*

    • @Eli-uo7nj
      @Eli-uo7nj 5 років тому +45

      Vsauce machine broke

  • @farn0153
    @farn0153 5 років тому +3575

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

  • @obisidian9243
    @obisidian9243 4 роки тому +1908

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

  • @swfreak258
    @swfreak258 4 роки тому +905

    The way Michael draws the symbol for infinity is unsettling

  • @CyclopsToppingWolverine
    @CyclopsToppingWolverine 5 років тому +851

    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

  • @mdrzn
    @mdrzn 5 років тому +1341

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

  • @Epinardscaramel
    @Epinardscaramel 5 років тому +1436

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

  • @commenturthegreat2915
    @commenturthegreat2915 5 років тому +2312

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

    • @DevilsBeefCake
      @DevilsBeefCake 4 роки тому +14

      Nah

    • @VarxenCore9
      @VarxenCore9 4 роки тому +41

      DONG was the previous name for this channel bruh

    • @commenturthegreat2915
      @commenturthegreat2915 4 роки тому +224

      @@VarxenCore9 r/woooosh

    • @gamerwizard69
      @gamerwizard69 4 роки тому +30

      @@commenturthegreat2915 yeah that was a bigass woosh, you beat me to it

    • @VarxenCore9
      @VarxenCore9 4 роки тому +8

      @@commenturthegreat2915 nice try lmao

  • @JohnDiggle21
    @JohnDiggle21 5 років тому +905

    I miss the "Hey Vsauce Michael here"

    • @lifestormer1051
      @lifestormer1051 5 років тому +2

      John Diggle you liking season 7 of arrow?

    • @northieee
      @northieee 5 років тому +12

      All of the things this man has brought for us to see and this is the observation that caught your attention.

    • @renejotas
      @renejotas 5 років тому +1

      Xvideos box?

    • @JohnDiggle21
      @JohnDiggle21 5 років тому

      @@lifestormer1051 yeah i have, but i have enjoyed the crossover even more, especially the thing that Earth-90 Flash said to Diggle, and of course the title card for the crossover next season

    • @plaguedoctor5097
      @plaguedoctor5097 5 років тому +2

      Everyone does

  • @blockhead134
    @blockhead134 3 роки тому +519

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

    • @sappy9320
      @sappy9320 2 роки тому +27

      maybe we're all small little islands too

    • @ColinPaddock
      @ColinPaddock 2 роки тому +24

      Full of increasingly tiny islands

    • @zzztriplezzz5264
      @zzztriplezzz5264 2 роки тому +16

      @@ColinPaddock and squiggly, spiderweb-like sand lines the closer you get

    • @keonscorner516
      @keonscorner516 2 роки тому +4

      @@ColinPaddock no the Mandelbrot set is all connected

    • @mathsciencefancier
      @mathsciencefancier Рік тому +4

      Yeah, it reminds me of an universe, or multiverse or cosmos, whatever our world.

  • @natepolidoro4565
    @natepolidoro4565 4 роки тому +143

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

    • @ermlerml7925
      @ermlerml7925 Рік тому +7

      And in school it'd take like years

  • @ChrisKogos
    @ChrisKogos 4 роки тому +930

    Please do a video on The Mandelbruh Set!

  • @drockomoush
    @drockomoush 5 років тому +856

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

  • @powerstation0872
    @powerstation0872 5 років тому +327

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

  • @johnchessant3012
    @johnchessant3012 3 роки тому +67

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

    • @Perririri
      @Perririri 3 роки тому +2

      #ThomasDolby *has entered the chat*

  • @spaghetti4245
    @spaghetti4245 3 роки тому +79

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

    • @carealoo744
      @carealoo744 2 роки тому +5

      He's smart enough to know how to have fun:)

  • @rorysnow7937
    @rorysnow7937 5 років тому +585

    3:29 meme gold

  • @Pxxnks
    @Pxxnks 5 років тому +438

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

    • @KingHeadbang
      @KingHeadbang 5 років тому +52

      Don't pretend you didn't like it.

    • @novafawks
      @novafawks 5 років тому +5

      Ding my dong mommy OwO

    • @topa9487
      @topa9487 5 років тому +1

      @@KingHeadbang wanted to reply that

    • @_albedo_7704
      @_albedo_7704 5 років тому +6

      But I'm more of a *Dong* dinger.

    • @jackshoemaker9023
      @jackshoemaker9023 5 років тому +3

      You touch my tralala... my ding ding dong...

  • @emanuelldaluzcaminha9122
    @emanuelldaluzcaminha9122 3 роки тому +23

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

    • @birdydragon
      @birdydragon 3 роки тому

      One of my favorite statements about it!

  • @user-rs3lg6un4n
    @user-rs3lg6un4n 5 років тому +40

    9:36 was an absolutely incredible moment

    • @chriskrausesmovie
      @chriskrausesmovie 8 місяців тому

      omg was your life changed...omg mine was too omg

  • @lytethekyte
    @lytethekyte 5 років тому +278

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

  • @feliscatusgaming3158
    @feliscatusgaming3158 5 років тому +1723

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

    • @funnr
      @funnr 5 років тому +74

      Gangster 2:don’t worry he coo

    • @feliscatusgaming3158
      @feliscatusgaming3158 5 років тому +53

      @@funnr Gangster 1:Aight then

    • @KaliTakumi
      @KaliTakumi 5 років тому +9

      "Gangster"

    • @KaliTakumi
      @KaliTakumi 5 років тому +12

      @Sassy The Sasquatch Remember when people stopped using the word gangster to describe the other group a decade ago

    • @litigation_jackson
      @litigation_jackson 5 років тому +7

      @couchpotato
      sheeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeit

  • @karatehh6966
    @karatehh6966 5 років тому +279

    “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

  • @ursidae97
    @ursidae97 4 роки тому +189

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

    • @kaggapu
      @kaggapu 3 роки тому +1

      @RileyBeez Etyptian numerals: *moo*

  • @RexusprimeIX
    @RexusprimeIX 5 років тому +213

    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.

  • @HamzaElkhatib
    @HamzaElkhatib 5 років тому +249

    9:44 it’s like he wants to be memed

    • @Hema8551
      @Hema8551 5 років тому +3

      Bec he wants?????????????????????

    • @Templarfreak
      @Templarfreak 5 років тому +32

      Michael has always been a weird guy. He was literally the main character of a music video called Bearded Nun that was a aprody of Lady Gaga's Judas.

    • @connorcriss
      @connorcriss 5 років тому +2

      I think he does tbh

    • @necromancer2367
      @necromancer2367 5 років тому

      Yes he does

    • @viciousviego2478
      @viciousviego2478 5 років тому

      Ikr 😂😜

  • @fun_nuggets2514
    @fun_nuggets2514 4 роки тому +26

    00:34 I think Michael is officially insane

  • @SahhiiChannel
    @SahhiiChannel 5 років тому +33

    7:26 onederful

  • @whcw11
    @whcw11 5 років тому +418

    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

  • @simonockas
    @simonockas 5 років тому +2063

    This Michael seems cool. He should start a UA-cam channel!

    • @TheRealQuenny
      @TheRealQuenny 4 роки тому +178

      Yeah I know and it should be called Vsauce because it’s sounds cool

    • @shoe_consumer5209
      @shoe_consumer5209 4 роки тому +99

      This other cool guy ironically named Michael has taken that name

    • @limitlesssfs4392
      @limitlesssfs4392 3 роки тому +34

      @@bathbombman its a joke

    • @Starbare6882
      @Starbare6882 3 роки тому +23

      theBathbombMan r/wooosh

    • @Ldforthetree
      @Ldforthetree 3 роки тому +32

      @@Starbare6882 or maybe, @theBathbombMan KNEW that and you didnt pick up on the irony, making you whooshed

  • @zergy55
    @zergy55 4 роки тому +5

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

  • @therationale2289
    @therationale2289 4 роки тому +12

    3:29 the funniest thing Michael has ever done imo

  • @1293ST
    @1293ST 5 років тому +86

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

    • @munjee2
      @munjee2 5 років тому +8

      Why did you even get a 4k monitor in the first place

    • @dirtybongwater5751
      @dirtybongwater5751 5 років тому +5

      >owns GTX 1050 but runs games at 4k cos iz future and human eye is 10fps

    • @Rajat-Sharma1
      @Rajat-Sharma1 5 років тому

      @@dirtybongwater5751 how do you know that eyes is 10fps🤔

    • @trent5807
      @trent5807 5 років тому +6

      @@Rajat-Sharma1 Damnit. Every time someone talks about it, it goes down by 1 fps. We're going to be seeing life in the eyes of a photon if you aren't careful.

    • @Rajat-Sharma1
      @Rajat-Sharma1 5 років тому +1

      @@trent5807 I have already discussed that with many of my friends and they discussed with a yet larger group. All of us are now able to see in - 1345544554 fps 🤣

  • @cluckcluck236
    @cluckcluck236 5 років тому +284

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

    • @austinzupon
      @austinzupon 5 років тому +14

      Whunchun I’m glad I wasn’t the only one who saw that

    • @jesusthroughmary
      @jesusthroughmary 5 років тому +2

      I came to the comments to point this out, lol

    • @GodlessPhilosopher
      @GodlessPhilosopher 5 років тому +25

      Unfortunately it's misspelled on the giant version at 14:53 too.

    • @user-me7hx8zf9y
      @user-me7hx8zf9y 5 років тому +19

      oof, Cardiod.

    • @evanward4303
      @evanward4303 5 років тому +11

      He's to smert too make that mestake.

  • @josephmcluckie2512
    @josephmcluckie2512 3 роки тому +8

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

    • @theodoreklopman7057
      @theodoreklopman7057 3 роки тому +1

      I don’t think so because there isn’t an infinitely small piece in real life

  • @thatcrystalpie
    @thatcrystalpie 4 роки тому +14

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

  • @maximunnit
    @maximunnit 5 років тому +50

    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!

    • @zankumo
      @zankumo 5 років тому +5

      Yep. The giant framed poster says it too. Whoops!

  • @3ckitani
    @3ckitani 5 років тому +117

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

    • @2neutrino
      @2neutrino 5 років тому +1

      shut up

    • @FuNLpMeineURL
      @FuNLpMeineURL 5 років тому +9

      3:29

    • @-Sp1n
      @-Sp1n 5 років тому +1

      @Errl Shmirl
      This is science
      Not Religious sh*t

    • @-Sp1n
      @-Sp1n 5 років тому

      i

    • @rufo
      @rufo 5 років тому +10

      Actually, it is both real and imaginary... It's kind of complex...

  • @chrissie1057
    @chrissie1057 4 роки тому

    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!

  • @HuntressCody
    @HuntressCody 4 роки тому +7

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

  • @BruceCinema1337
    @BruceCinema1337 5 років тому +382

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

    • @elianagriffith9510
      @elianagriffith9510 5 років тому +1

      Oh boy.. isn't that awesome?

    • @imaginerus
      @imaginerus 5 років тому +4

      9:42

    • @appleislander8536
      @appleislander8536 5 років тому +1

      I can't believe I never noticed the signs before now. His sanity has been slowly dripping away for years...

    • @georgeharrold5423
      @georgeharrold5423 5 років тому +2

      Im not sayin anything but ive seen people on coke and he might be on it😂

    • @svz5990
      @svz5990 7 місяців тому

      ​@@appleislander8536his first vsauce videos were more like silly vsauce studio bloopers

  • @av4787
    @av4787 5 років тому +29

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

    • @av4787
      @av4787 5 років тому

      @M. de k. You do miss your ex if you broke up. You do miss her, girlfriend or not her.
      (Please dont say you dont, maybe you don't, this is just a example, don't sue me)

    • @av4787
      @av4787 5 років тому

      @@rawpie2 bruh have you played watch dogs

  • @greysonmiller9407
    @greysonmiller9407 5 років тому +8

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

  • @ayem9504
    @ayem9504 4 роки тому +4

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

  • @matthewpapa5529
    @matthewpapa5529 5 років тому +7

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

  • @weibull760
    @weibull760 5 років тому +634

    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.

    • @cellardoor7500
      @cellardoor7500 5 років тому +13

      Jason Vint well said!

    • @user-iu1xg6jv6e
      @user-iu1xg6jv6e 5 років тому +28

      I used to respect them until they started mind field and curiosity box .
      It appears that money is more important for them than sharing interesting ideas and knowledge. I think they stopped posting in main channel to promote mind field. And look how he tease us in what inside the box which cost much for lot of viewers.
      He went that low to advertise the box.

    • @SirTatManTat
      @SirTatManTat 5 років тому +195

      Dude This poster is raising money for Alzhiemers research, Mind field allows him to do larger scale projects, and the curiosity box is a nice little gift for kids, i don't get why any of this is a bad thing.
      People have similar ideas all the time, they don't have to be ripping eachother off.

    • @WinterandNoodle
      @WinterandNoodle 5 років тому +17

      SirTatmanTat No dude, the poster is a ripped off. It even has the grid in the water like the original map has, just inaccurate because it didn't fit in the scale. The curiosity box isn't even a good box, it's mostly filled with random items that have no relevancy or anything to play with. Mind field is just arm-chair psychology show. And charity doesn't work, the money usually goes into the revue than the research itself.

    • @noobpro9759
      @noobpro9759 5 років тому +85

      @@WinterandNoodle cynicism at its finest ladies and gentlemen. It a box of things that (if you're actually into this kind of stuff) makes you think and could possibly get you thinking about various forms of science. It doesn't have to be something that physically entertains you. What are you 5? Do you need jingly keys in your face?
      Mindfield i haven't really watched so i can't say much about that.
      And you have no clue what they do with their money unless you have somehow hacked into their records soooo.

  • @johnrock401
    @johnrock401 4 роки тому +1

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

  • @tooblis
    @tooblis Рік тому +4

    10:40
    Michael is so cute here

  • @charissaschoon9206
    @charissaschoon9206 5 років тому +29

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

  • @funnr
    @funnr 5 років тому +277

    WHADDUP DING DONGERS

    • @naufalap
      @naufalap 5 років тому +1

      I spent more time than I would admit clicking left arrow button repeatedly on that part.

    • @Kommunistpartiet
      @Kommunistpartiet 5 років тому +1

      FibeVideo you forgot the asterisks

    • @micheleac66
      @micheleac66 5 років тому +1

      FibeVideo hey I have one of those

    • @nullset2
      @nullset2 5 років тому +1

      WADDUP HILA KLEINERS

    • @marcocampobello7981
      @marcocampobello7981 5 років тому +2

      9:47

  • @WhiskyLima
    @WhiskyLima 4 роки тому

    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!

  • @boluaygepong5920
    @boluaygepong5920 5 років тому

    Michael you're actually living your best life

  • @jesssald
    @jesssald 5 років тому +2124

    When will you do a face reveal?

    • @eggy543
      @eggy543 5 років тому +36

      Michael done that a couple of years ago!

    • @danii7120
      @danii7120 5 років тому +324

      Don't pressure him. He'll do it soon, you know how shy he is.

    • @jesssald
      @jesssald 5 років тому +78

      Don't be so *Eggy* 🤣🤣🤣

    • @eggy543
      @eggy543 5 років тому +13

      @@danii7120 *facepalm* Are you looking at the screen?!

    • @avathy9813
      @avathy9813 5 років тому +175

      Eggy543
      r/woooosh

  • @theredfire14
    @theredfire14 5 років тому +316

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

    • @jerrettneandermeier9091
      @jerrettneandermeier9091 5 років тому +8

      Luckyeti you only need to do that if z is accompanied by a coefficient.

    • @pavlevilotijevic7266
      @pavlevilotijevic7266 5 років тому +7

      Thank goodness somebody pointed that out!

    • @EricM818
      @EricM818 5 років тому +20

      @@jerrettneandermeier9091 It does have a coefficient, -1.

    • @nagatotzu8681
      @nagatotzu8681 5 років тому +1

      @@EricM818 so if -1 is the coefficient....which number is the power squaring

    • @anywallsocket
      @anywallsocket 5 років тому +23

      @@nagatotzu8681 -1^2 =/= (-1)^2 - hence the utility of parenthesis

  • @SloaneGrey
    @SloaneGrey 5 років тому

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

  • @jacobthomas2948
    @jacobthomas2948 5 років тому

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

  • @hammad8707
    @hammad8707 5 років тому +105

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

    • @foty8679
      @foty8679 5 років тому +8

      No. He explained it in a mindfield video. He will upload again on Vsauce at sometime.

    • @gogogo123454321
      @gogogo123454321 5 років тому

      @@foty8679 Nah he's right.

    • @something7836
      @something7836 5 років тому

      @@gogogo123454321 no.

    • @aboriani
      @aboriani 5 років тому

      FotY yeah, he said that 2-3 years ago....

  • @fomod_
    @fomod_ 5 років тому +616

    I wish you'd just continue uploading on Vsauce

  • @Crabs69
    @Crabs69 Рік тому

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

  • @peril7531
    @peril7531 5 років тому +114

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

  • @JimbobH
    @JimbobH 5 років тому +12

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

  • @AspienPadda
    @AspienPadda 5 років тому +55

    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.

    • @saqibmudabbar
      @saqibmudabbar 5 років тому +12

      We all love you ❤️ Don’t worry

    • @AspienPadda
      @AspienPadda 5 років тому +6

      Hey thanks @@saqibmudabbar that's really sweet to say! I love you too!

    • @imXarys
      @imXarys 5 років тому +17

      DONG's comment section is truly a beautiful place. We all love eachother. And knowledge.

    • @AspienPadda
      @AspienPadda 5 років тому +6

      Definitely @@imXarys this is a great space. Few videos have such intelligent and loving communities like those of Michael and the Vsauce guys.

    • @saqibmudabbar
      @saqibmudabbar 5 років тому +2

      I hope you’re doing great! Here’s a hug from me. 🤗
      Here’s a lovely video from my country, it will make your day, I promise.
      ua-cam.com/video/mH227HILqII/v-deo.html
      Find me in the comment section there 🥰

  • @aikenanderson22
    @aikenanderson22 3 роки тому +7

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

  • @fartballs4905
    @fartballs4905 2 роки тому +1

    I seriously find more comedy in this than any other channel on UA-cam

  • @gabrieletsgo1218
    @gabrieletsgo1218 5 років тому +162

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

  • @Zeldaschampion
    @Zeldaschampion 5 років тому +30

    Eye witnessing Micheal's transformation into Kratos.

  • @obisidian9243
    @obisidian9243 4 роки тому +4

    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.

  • @alejandro_pacho
    @alejandro_pacho 4 роки тому +4

    3:08 that lick tho

  • @mebamme
    @mebamme 5 років тому +108

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

    • @Zeph_
      @Zeph_ 5 років тому +8

      i think it is

    • @ChazCharlie1
      @ChazCharlie1 5 років тому

      I thought so too!

    • @FractalWoman
      @FractalWoman 5 років тому +2

      @@ChazCharlie1 Yup. CARDIOID is the correct spelling.

  • @TheGoupil19
    @TheGoupil19 5 років тому +32

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

  • @jackstewart8406
    @jackstewart8406 5 років тому +6

    I said wow exactly when wow flashed up and got completely spooked. I said wow again just to make sure I wasn't being watched

  • @thebreadhead7501
    @thebreadhead7501 4 роки тому +5

    3:39 *confused screaming

  • @ArianSadrayi
    @ArianSadrayi 5 років тому +5

    1:55 when Michael suddenly gets possessed by Jake.

  • @camelopardalis84
    @camelopardalis84 5 років тому +489

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

    • @falcon-vx3cc
      @falcon-vx3cc 5 років тому +2

      It's not mentioned

    • @ekn_38
      @ekn_38 5 років тому +29

      Commented the same,just saw yours recently and deleted mine

    • @camelopardalis84
      @camelopardalis84 5 років тому +6

      @@ekn_38 Must have been *VERY* recently since the video was uploaded maybe half an hour ago! I knew I had to be fast so I posted the comment while still watching the video. I mean, it's not like a English speaking channel with so many subscribers could ever not have a lot of viewers who know German.

    • @camelopardalis84
      @camelopardalis84 5 років тому +3

      @@falcon-vx3cc
      Thanks! I was about to fall asleep watching the video before and then stopped it when I thought I would be out in within a few seconds. I'm still tired but completely awake again.

    • @leonardjanke2855
      @leonardjanke2855 5 років тому +5

      Madelbrot ist das beste brot

  • @blinkecho
    @blinkecho 5 років тому +2

    3:17 is why I love Michael

  • @edenb329
    @edenb329 Рік тому

    i like the ability to zoom/hone-in on differences in fractally complex-sets. it reminds me of our ability to seemingly infinitely zoom IRL, down to quarks and such.

  • @NobodyXChallengerYT
    @NobodyXChallengerYT 5 років тому +432

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

    • @theTavis01
      @theTavis01 5 років тому +111

      I think so too! But they won't even return my messages...

    • @TroyWuelfing
      @TroyWuelfing 5 років тому +45

      @@theTavis01 I have ordered your poster because its beautiful and i wanted you to have some money for your art and add something my visitors wont understand to my wall. also i hope that Michael reaches out to you and makes this right. he seems like a good guy so lets hope he does the right thing.

    • @theTavis01
      @theTavis01 5 років тому +28

      @@TroyWuelfing Thank you for the support!

    • @theTavis01
      @theTavis01 5 років тому +8

      @@loremipsum313 that's awesome!

    • @euleer.-.9385
      @euleer.-.9385 4 роки тому

      @@theTavis01 did they contact you?

  • @ryandaley1402
    @ryandaley1402 5 років тому +3

    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.

  • @clickbaitpolice9792
    @clickbaitpolice9792 3 роки тому

    ty for this. been seeing this in a lot of "Scale past the universe" videos and didnt know wtf was going on

  • @summerlakephotog8239
    @summerlakephotog8239 2 роки тому

    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❗️😊👍

  • @dbarr49
    @dbarr49 5 років тому +41

    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.

    • @gogogooner
      @gogogooner 5 років тому +1

      Yes, you are the Messiah and we will forever eat up anything you produce!

  • @1976Joachim
    @1976Joachim 5 років тому +131

    Isn't it cardioid instead of Cardiod?

    • @c0rtikoZteroids1
      @c0rtikoZteroids1 5 років тому +1

      That is correct

    • @charonder
      @charonder 5 років тому

      Oof

    • @Madmagicanman1
      @Madmagicanman1 5 років тому

      Yep. Probably my biggest gripe with the map Michael's showing here, but otherwise it's solid

    • @theTavis01
      @theTavis01 5 років тому +5

      @@Madmagicanman1 they also totally made up the equipotential lines and external rays that make up the grid in the water... they only put them in there because they look so good on my original Mandelmap poster, except that I actually solved for them and drew them correctly! So yeah, other than the huge obvious typo, the made-up grid lines, and the fact that he totally copied my idea without giving even the slightest hint of a shout-out, it does actually look pretty decent I'll give it that.

    • @davetir
      @davetir 5 років тому +1

      Ouch! Proofreading Pays!

  • @100kleitung7
    @100kleitung7 5 років тому +29

    9:00 shouldn't it be (-1)^2 rather than -1^2

    • @luhdooce
      @luhdooce 4 роки тому +4

      @@tessenary_ no it's not

    • @SoI-
      @SoI- 4 роки тому

      @@tessenary_ put in your calculator -1*-1

    • @omarcaballero2011
      @omarcaballero2011 4 роки тому

      @@SoI- bro -1² means -(1²)

    • @SoI-
      @SoI- 4 роки тому

      @@omarcaballero2011 just like 1^2 is 1^2^2

    • @ViratKohli-jj3wj
      @ViratKohli-jj3wj 3 роки тому +1

      Both are same

  • @bobbyv3
    @bobbyv3 2 роки тому

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

  • @BernardoMarquesIdeia
    @BernardoMarquesIdeia 5 років тому +224

    3:29 My man Michael just pulled a Pewdiepie

  • @Nugcon
    @Nugcon 5 років тому +329

    Hello fellow Ding Dongers in the comment section.

  • @wallybeery4058
    @wallybeery4058 3 роки тому

    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!

  • @lubibubi6380
    @lubibubi6380 2 роки тому

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

  • @HTPCYMC
    @HTPCYMC 5 років тому +1086

    Hey Michael, Vsauce here

    • @greenoleeno3793
      @greenoleeno3793 5 років тому +70

      Wow, this comment is very thoughtful, funny, and original. It really relates to the meaning of the video and it's not a dead unfunny joke related to the person in the video. Man, people from SiIvaGunner and people that are everywhere are very funny. Those sans memes and those anime memes are just philosophical. I feel like Shakesphere loves those niko niko niis, and those sprite cranberries. I think you should be nominated for Oscar.

    • @straightbussin
      @straightbussin 5 років тому +2

      maximum maxerz you said it

    • @unintelligible3985
      @unintelligible3985 5 років тому +6

      wat up ding-dongers

    • @kapjoteh
      @kapjoteh 5 років тому +2

      lul 21 hmm it’s almost like he uses like bots, because no one likes him or his comments

    • @yatint9665
      @yatint9665 5 років тому +2

      @@greenoleeno3793
      FEEL THE PAIN IN THOSE WORDS!

  • @rodrigovillanueva5384
    @rodrigovillanueva5384 5 років тому +52

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

  • @parrotlord7393
    @parrotlord7393 3 роки тому

    As soon as I’ve seen the title I know everything about that shape.

  • @mistirion4929
    @mistirion4929 3 роки тому +8

    For everyone thinking "Why the hecc would someone ever need complex numbers?"
    Try to study electrical engineering, it's kind of important there. It's also pretty easy but the connection between reality and theory is kinda hard to figure out

  • @GoikOShea
    @GoikOShea 5 років тому +23

    Take a point named C in the complex plane
    And let Z1 be Z squared plus C
    And Z2 is Z1 squared plus C
    And Z3 is Z2 squared plus C and so on
    If the series of Zs will always stay
    Close to Z and never trend away
    That point is in the Mandelbrot Set

    • @RRM_Personal
      @RRM_Personal 5 років тому +1

      Yay! Jonathan Coulton!

    • @Vesperon
      @Vesperon 5 років тому

      @@RRM_Personal wow it totally is....i miss his music

  • @NewbyTon
    @NewbyTon 5 років тому +175

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

    • @namelessLesbian
      @namelessLesbian 5 років тому +4

      Ding dongers

    • @rooivalk1
      @rooivalk1 5 років тому +4

      Ding my Dong fellow ding dongers

    • @EpicRainbowLollipop
      @EpicRainbowLollipop 5 років тому +1

      michael started his youtube career by shitposting so i'm not surprised tbh

    • @bojackson3073
      @bojackson3073 5 років тому +1

      EpicRainbowLollipop shitposting.. whats your favorite social media? reddit?

  • @TheFishKing64
    @TheFishKing64 3 роки тому

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

  • @FinlayHamm
    @FinlayHamm 3 роки тому +1

    Happy birthday to the mandelbrot guy

  • @cormacsmithy3975
    @cormacsmithy3975 5 років тому +3

    He is the pewdiepie of science channels

  • @LittleBitVic
    @LittleBitVic 5 років тому +22

    "Mandelbrot Set, you're a Rorschach Test on fire.
    You're a day-glo pterodactyl.
    You're a heart-shaped box of springs and wire.
    You're one badass fracking fractal!
    And you're just in time to save the day~
    Sweeping all our fears away~
    You can change the world in a tiny way..."
    --Jonathan Coulton

    • @mustardpuddle
      @mustardpuddle Рік тому +1

      "If you ever lose your way,
      A butterfly will flap its wings from a million miles away...
      and a little miracle will come to take you home"
      --JoCo

    • @moosesurgeon
      @moosesurgeon 11 місяців тому

      ​@@mustardpuddle "Just take a point called Z in the complex plane
      Let Z1 be Z squared plus C
      And Z2 is Z1 squared plus C
      And Z3 is Z2 squared plus C
      And so on
      If the series of Z's should always stay
      Close to Z and never trend away
      That point is in the Mandelbrot Set"

  • @adrianajohnson9632
    @adrianajohnson9632 2 роки тому

    Soooo awesome! Thank you!!

  • @jessethomas9676
    @jessethomas9676 4 роки тому +1

    I got that poster from amazon last week. Been watching vsauce for years, never knew this video existed