Fibonacci Numbers hidden in the Mandelbrot Set - Numberphile

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  • Опубліковано 15 гру 2024

КОМЕНТАРІ • 1,1 тис.

  • @raspi1983
    @raspi1983 7 років тому +837

    'B.' in Benoit B. Mandelbrot's name stands for Benoit B. Mandelbrot

    • @Paine137
      @Paine137 7 років тому +9

      raspi1983 Old joke.

    • @jony4real
      @jony4real 7 років тому +11

      Wait, so what does the second 'B.' stand for? :-)

    • @martinmartinmartin2996
      @martinmartinmartin2996 7 років тому +44

      the second "B" stands for Benoit B. Mandelbrot
      observerms

    • @Pacvalham
      @Pacvalham 7 років тому +13

      ua-cam.com/video/laHl-aFZUJI/v-deo.html The EDM in EDM Detection Mode stands for EDM Detection Mode.

    • @rcredidio
      @rcredidio 7 років тому +5

      I saw what you did there :)

  • @prime2920
    @prime2920 4 роки тому +48

    It is so interesting how literally everything in math is connected and intertwined. This is really cool because if you don’t quite understand a certain topic or problem you can look at some things you do understand and connect it to what you are having trouble with.

    • @waynedarronwalls6468
      @waynedarronwalls6468 2 роки тому +3

      That is the essence of what is known as the Langlands Program, named for Robert Langlands, who essentially created the whole schema...it relates to what are two entirely separate fields in mathematics, harmonic analysis and number theory, and the bridge that links them together.

    • @EquaTechnologies
      @EquaTechnologies 11 місяців тому

      EXACTLY! I also find fascinating how this figure is encoded in math and anywhere you go in the universe, the figure is still the same!

  • @kevnar
    @kevnar 7 років тому +127

    This video about Fibonacci numbers was as good as the last two combined!

    • @knvids2812
      @knvids2812 Рік тому +4

      not going to like because likes are at a fibonacci number

    • @benloud8740
      @benloud8740 8 місяців тому +1

      Underrated comment

  • @Kowzorz
    @Kowzorz 7 років тому +72

    Everything about this video was great! The visuals were tuned perfectly. The explanation was thorough but succinct. And the enthusiasm of the presenter really brings it all together. Great work!

  • @Tehom1
    @Tehom1 7 років тому +30

    7:20 Sometimes called the "naive sum" as well. It's also how you construct the Stern-Brocot tree, which enumerates all the positive rational numbers without repeating any.

  • @adavewiley
    @adavewiley 7 років тому +701

    Kudos to the animator. The scuttling mandelbug was a delight.

    • @trucid2
      @trucid2 7 років тому +30

      David Wiley The sound and the animation cracked me up.

    • @Lucaazade
      @Lucaazade 7 років тому +49

      No it was in fact the very opposite of a delight .

    • @qwertyasdf66
      @qwertyasdf66 7 років тому +17

      Yusss. I came down here to find the comments about it. That made me so happy. 4:24

    • @requemao
      @requemao 6 років тому +4

      It's a Miyazaki Mandelbug!

    • @snbeast9545
      @snbeast9545 6 років тому +2

      It's a Scuttlebug jamboree.

  • @simoncarlile5190
    @simoncarlile5190 7 років тому +472

    Two of my favorite concepts in one video. Today is looking like a good day.

    • @busTedOaS
      @busTedOaS 7 років тому +56

      Women and Paper?

    • @jacobshirley3457
      @jacobshirley3457 7 років тому +21

      Audio and Visual Stimulation

    • @me_hanics
      @me_hanics 7 років тому +6

      fibonacci and grills

    • @HiItsSalty
      @HiItsSalty 7 років тому +12

      markers and brown paper?

    • @rmm2000
      @rmm2000 6 років тому +1

      Fibonacci Numbers make it 3!

  • @mamoonblue
    @mamoonblue 7 років тому +1339

    I lost her at 1+1 is 2.

    • @teovinokur9362
      @teovinokur9362 7 років тому +34

      Nathan Thames
      That's kind of Numberphile's comment section in a nutshell

    • @JK-ff8xf
      @JK-ff8xf 7 років тому +3

      "PewDiePie's personal account" kek

    • @EvanRustMakes
      @EvanRustMakes 7 років тому +30

      Muhammad Mamoon 2+2 is 4, -1 is 3, quick maths

    • @deschain1910
      @deschain1910 7 років тому +4

      Well, you have the basics down.

    • @KnakuanaRka
      @KnakuanaRka 6 років тому +1

      Who thinks that’s funny?!!

  • @CrucialMuzic
    @CrucialMuzic 7 років тому +195

    Wow mind *BLOWN,* this is amazing
    Who else just wanted it to keep on zooming in until infinity? [8:41]

    • @sebastianelytron8450
      @sebastianelytron8450 7 років тому +12

      You mean an infinitely long UA-cam video? No thanks.

    • @ZipplyZane
      @ZipplyZane 7 років тому +2

      Yeah. I wish it would've just kept doing numbers and faded out, to create the impression it could go on forever. Stopping makes it look like it fails at that number.

    • @sebastianelytron8450
      @sebastianelytron8450 7 років тому +7

      Nobody with half a brain thought it "failed" at that number

    • @SapphicRain
      @SapphicRain 7 років тому +11

      Here's one of the deepest zooms fellow Mandelbrot enthusiast ua-cam.com/video/0jGaio87u3A/v-deo.html

    • @littleboylost1o1
      @littleboylost1o1 7 років тому

      +

  • @OlafDoschke
    @OlafDoschke 7 років тому +19

    I love the little slot machine illustrating the iteration and the ping sound it makes. That's the way Mandelbrot sets should be computed.

  • @AntonioKowatsch
    @AntonioKowatsch 7 років тому +195

    Holly's laugh touches my cardioid :P

  • @meanmreen
    @meanmreen 7 років тому +155

    Every time I’m feeling particularly sharp or intelligent, I click on one of these videos and it instantly puts me back in my place 😅
    Still, for my limited understanding in advanced math, it was quite interesting.

  • @PlayTheMind
    @PlayTheMind 7 років тому +932

    Riemann: My zeta function hides primes
    Mandelbrot: My set hides Fibonacci
    Ramanujan: -1/12 __

    • @SparHD
      @SparHD 7 років тому +66

      PlayTheMind riemann is way above mandlebort and ramanujan

    • @AryanTheMentalist
      @AryanTheMentalist 7 років тому +2

      Sharklops Haha.. nice one

    • @livedandletdie
      @livedandletdie 7 років тому +16

      What do you mean wrong, the limit of the nonconvergent sum of 1+2+3+4+5...+n where n=Alephnull-1 Does end up as -1*(1/12)

    • @DABATTLESUIT
      @DABATTLESUIT 7 років тому +20

      jawad mansoor YOU CANT JUST MAKE THAT CLAIM AND LEAVE

    • @SparHD
      @SparHD 7 років тому +18

      +jawad mansoor Riemann has done much more besides his hypothesis eg: introduced the term manifolds, riemann integrals, was one of the pioneers of non euclidian geometry (with gauss and some other russian guy), also physics and probably tons of things that im not aware of, he was one of the best mathematicians to ever live

  • @albertb8999
    @albertb8999 7 років тому +186

    It's pretty cool, that these two things have such a connection

    • @Nukestarmaster
      @Nukestarmaster 7 років тому +10

      But not terribly surprising, Fibonacci numbers pop up just about anywhere.

    • @albertb8999
      @albertb8999 7 років тому +20

      Nukestarmaster
      I
      do
      not
      think
      so_about
      these_numbers!
      Fibonacci_numbers_are
      definitely_not_anywhere,_you_idiot

    • @jpphoton
      @jpphoton 7 років тому +8

      it leads me to speculate that *everything* is, in fact, encoded in the Mandelbrot Set.

    • @MarsLonsen
      @MarsLonsen 6 років тому

      fukin druggos

    • @HeartAndMind34
      @HeartAndMind34 5 років тому +1

      @@albertb8999 I see what you did there, incorporating the sequence into your sentences.
      Well played, Albert B, well played.

  • @tgwnn
    @tgwnn 7 років тому +426

    She's so cool!

  • @trailtrs1
    @trailtrs1 4 роки тому +8

    This is one of the very best layouts of this fractal relationship with the Fibonacci sequence

  • @aardvarkman6919
    @aardvarkman6919 7 років тому +23

    The beauty of this math overwhelms me with emotion. Perhaps that seems strange, but the beauty of how all this works out makes me want to cry.

    • @justaphotographer
      @justaphotographer 3 роки тому +3

      I thought I was the only one who feels this way! I completely agree! There is just so much order and beauty in all the world I don’t know how to take it all in emotionally.

  • @mathsmoica
    @mathsmoica 7 років тому +268

    *The reason I love mathematics*

    • @microbuilder
      @microbuilder 7 років тому +6

      "Is the universe a fractal that can be calculated in equation?
      Is it Fibonaccis perfect golden spiral or is it just my imagination?"

    • @kennethwalker3939
      @kennethwalker3939 5 років тому +1

      From what I can tell, the world is defined by mathematics and patterns naturally. Math is the translation for the patterns that took the chaos or the earliest known parts of the universe up till as far as we can see. When Mathematics fails is the day I'm lost lol. @@microbuilder

    • @aarongoodwin4845
      @aarongoodwin4845 3 роки тому +1

      Beautiful Ladies teaching us?🤫

    • @realeyesrealisereallies97
      @realeyesrealisereallies97 2 роки тому

      Peng broads?

  • @Wayne_Robinson
    @Wayne_Robinson 4 роки тому +4

    Despite being quite familiar with both the Fibonacci sequence and the Mandelbrot set, my mind was indeed blown. It's even more amazing how "number games" like this can relate to the physical world (at least the one we can perceive).

  • @Cyberspine
    @Cyberspine 7 років тому +942

    I would tell a joke about Fibonacci.
    But it's as bad as the two previous jokes you heard combined.

    • @wierdalien1
      @wierdalien1 7 років тому +6

      Cyberspine #groan

    • @raphielohnef4678
      @raphielohnef4678 7 років тому +21

      You shouldn't start with two zeros... :D

    • @Grizzlywer
      @Grizzlywer 7 років тому +6

      0 + 0 = 0

    • @bradleylomas7525
      @bradleylomas7525 5 років тому +2

      Cyberspine and where does your joke end? If you are going to be funny, at least have an educated punch line to go with it. Those are hilarious

    • @josuke6869
      @josuke6869 5 років тому +2

      @@bradleylomas7525 HAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHAHHAHAHAHAHAHAHAHAHA AHBAHSBHABSH HAHAHAHAHAHAH

  • @RicardoRoblesJr
    @RicardoRoblesJr 6 років тому +4

    Thanks for the incredibly fascinating video. The more I learn about the Mandelbrot set, the more I like it. Dr. Krieger is excellent as always.

  • @gabrielthompson9800
    @gabrielthompson9800 4 роки тому +20

    Test question: In the Fibonacci sequence 1, 1, 2, 3, 5, 8, 13, what would be the next number?
    Answer: So you take a point called c on the complex plane...

    • @philpayton8965
      @philpayton8965 4 роки тому

      So is not a valid word with which to start a sentence except in very rare circumstances, for example explaining the purpose of doing something.

    • @nodezsh
      @nodezsh 2 роки тому

      @@philpayton8965 It is valid for a joke though. The joke was that he's explaining a very easy concept in the most complex way imaginable using the most casual language possible.

    • @philpayton8965
      @philpayton8965 2 роки тому

      @@nodezsh sorry man it was a bit pedantic of me it just used to be a pet hate of mine, probably fuelled by the fact I had a horrible micro-managing supervisor who started every sentence with "So...".
      it was a me problem, not a you problem, just ignore me. was a long time ago now anyway.

  • @wntu4
    @wntu4 7 років тому +63

    A new video of Dr. Holly, aka she who commands my heart, mind and soul. This is a great week indeed.

  • @cobaltbluesky2276
    @cobaltbluesky2276 6 місяців тому +1

    i was obsessed with the fibonacci sequence when i was little and i'm obsessed with the mandelbrot set now, seems like a perfect video for me lol

  • @CountKoski
    @CountKoski 7 років тому +6

    These inserted animations make all the difference - great thinking mr Haran!

    • @numberphile
      @numberphile  7 років тому +6

      Glad you liked them - they were done by Pete McPartlan

  • @MikeReggie95
    @MikeReggie95 5 років тому +1

    What I've learnt is no matter how many Mandelbrot videos I watch, I still have no idea how it's made. Only that it looks amazing on a projector!

  • @billburr1347
    @billburr1347 7 років тому +205

    Intelligence makes people more beautiful

    • @NwoDispatcher
      @NwoDispatcher 5 років тому +12

      Racial purity makes humanity beautiful

    • @NwoDispatcher
      @NwoDispatcher 4 роки тому

      @AccuracyIsGone I agree... come go after the heretic of the g4y empire

    • @arthurmee
      @arthurmee 4 роки тому +6

      @@NwoDispatcher the exact opposite is true. Racial purity leads to an amplification of genetic defects over time. The largest gene pool is the healthiest.

    • @andrew7taylor
      @andrew7taylor 4 роки тому +5

      @@NwoDispatcher If you truly believe that, don't ever have a DNA testing. You'll find out that you're anything but.
      Most of your ancestors had more IQ than you and had this idea that screwing around is more fun than raging about a concept that doesn't exist.

    • @FrankACai
      @FrankACai 3 роки тому

      @@NwoDispatcher come on, evolution needs tension. How about you leave it be when it's so minor

  • @vizart2045
    @vizart2045 2 роки тому +1

    Numberphile really nails it by explaining math in an entertaining and lighthearted way.

  • @winmine0327
    @winmine0327 7 років тому +29

    Next: how to cut a cake via prime numbers, Graham's number created by Conway's game of life, and the fractal dimensions inside Parker squares.

    • @erik-ic3tp
      @erik-ic3tp 7 років тому

      Do you want existential crisises? Anyway, cool subjects!

    • @matttondr9282
      @matttondr9282 3 роки тому

      …while doing a dice trick represented by playing cards printed on the surface of a Klein bottle.

  • @FrankBatistaElJibaro
    @FrankBatistaElJibaro 2 роки тому +3

    Everytime Holly laughs a furry baby kitten is born.

  • @baptistebauer99
    @baptistebauer99 7 років тому +3

    Amazing.... please do more videos about the Mandelbrot set. It is the most interesiting mathematical object I know of, in my opinion...
    Loving your videos!

  • @RupertBruce
    @RupertBruce 5 років тому

    I wrote a program to generate the Mandelbrot set many years ago and the interesting part was outside the iconic shape - the colours are formed as visual representations of the number of iterations (like a contour map) with the iconic shape merely the set of values that kept on iterating. They were the boring bit! Thank you for showing me what I was missing. I'll have to revisit that code with these extra features to explore!

  • @maggiehernandezreni
    @maggiehernandezreni 5 років тому +22

    I used to hate Mathematics. Long story short I developed Arithmophobia since an early age. Until tonight I watched a video about Fibonacci Sequence that introduces me a total new prospective of Math into my life. And for the first time in a long time 33 years more or less (I'm actually 37) I understood Mathematics 😱🤯😍 And after that I found this video is like a double 🤯🤯 sorry I had to is literally mindblowing. I think I can start saying I HAD Arithmophobia. Thank you!

    • @nodezsh
      @nodezsh 2 роки тому

      I would 'guess'? it usually happens because of how cumbersome it is to get used to it from such a young age and to basically drill math into your skull by brute force.
      Maybe, for whatever reason you had a knack for math but never developed the skill to use it because of some bad experience learning it growing up, at a very critical time. But this here, this makes no sense. It's like finding a glitch in the matrix. That's why it's so fun.

  • @ibmicroapple9142
    @ibmicroapple9142 7 років тому +375

    oh yes, Holly Krieger

    • @dlee645
      @dlee645 7 років тому +28

      IBMicroapple There needs to be more Dr. Krieger videos.

    • @fantasick8880
      @fantasick8880 7 років тому +48

      I think I have a new crush.

    • @EVILVIKTOR
      @EVILVIKTOR 6 років тому +6

      @TheronQRamacharaka I'm guessing it's a perfect match. But something tells me the carpet is gone.

    • @takotaw8453
      @takotaw8453 4 роки тому +4

      IBMicroapple simp

    • @waynewalls5033
      @waynewalls5033 4 роки тому +1

      @@takotaw8453 still a virgin

  • @Manusmusic
    @Manusmusic 7 років тому +13

    Glad to see her again!

  • @shubhamshinde3593
    @shubhamshinde3593 7 років тому +42

    2:12 even non-mathematicians love this for different reasons xD

    • @Myrslokstok
      @Myrslokstok 7 років тому +6

      Shubham Shinde
      Yes it is fun. They kind of look down on us as children.

    • @pizeblu
      @pizeblu 4 роки тому +3

      When you really uncover it, it is for the same reasons, it is a way to describe or show the nature of the universe and consciousness. Just mathematicians see it in numbers and other people see it more spiritual, but it dissolves into the same sensations one has.

    • @raffaelepiccini3405
      @raffaelepiccini3405 4 роки тому +2

      @@pizeblu well.. except that the way mathematicians see it actually makes sense, the way you see it doesn't.. it really have nothing to do with consciousness, the nature of the universe... It's just math
      As a non matematician myself I love it because it shows how something so complex and weird can come up from such a simple rule.. also because fractals are just weird, counterintuitive and fascinating.. but nobody who understand this even a tiny bit would say that it's connected with things like consciousness or the nature of the universe.. get your feet on the ground mate

    • @ManlyBog6448
      @ManlyBog6448 4 роки тому +2

      @@raffaelepiccini3405 I just don't understand how so many people who had never communicated before are able to "figure out" fractals and how they relate to consciousness on their own.

  • @declinescore
    @declinescore 7 років тому +11

    2:13 made me smile

  • @Traumtheater0
    @Traumtheater0 7 років тому +41

    The Mandelbrot Set will never be as beautiful as Dr. Holly.

    • @Darker7
      @Darker7 7 років тому +5

      I disagree :Ü™

  • @marekbanaszkiewicz6338
    @marekbanaszkiewicz6338 7 років тому +9

    Mandelbrot set is amazing. It's incredible how quite simple definition leads to infinitively complex structure.

  • @beekarola
    @beekarola 7 років тому +1

    Great explanation, thanks. By this construction the numerators are also the Fibonacci sequence, two terms behind the denominators. Since the ratio of subsequent terms in the Fibonacci sequences approaches the Golden Ratio as n --> infinity, this means that the ratios that you are considering approach the Reciprocal of the Golden Ratio, Squared. [I think this is right - and surely pretty well known. I just realized it from your presentation.]

  • @Deathranger999
    @Deathranger999 7 років тому +18

    The picture of the freshman sum they showed was wrong. Is it a Parker freshman sum? 🤔

    • @Morstius
      @Morstius 5 років тому +4

      I was searching for the comment pointing that out, wonder who misunderstood the freshman sum joke

    • @mikeo759
      @mikeo759 5 років тому +1

      For some reason they showed the multiplicative

  • @WiggysanWiggysan
    @WiggysanWiggysan 7 років тому

    *NEW RECORD* - Congratulations Numberphille. Only 12 seconds to completely confuse every atom in my head.
    I await your next video.

  • @CybranM
    @CybranM 7 років тому +87

    I can see that nail and gear flag in the background :)

  • @Schnitz13
    @Schnitz13 4 роки тому

    This channel never ceases to amaze me.

  • @Mobin92
    @Mobin92 7 років тому +111

    So I guess it's time to fall in love again...

  • @djcarter85
    @djcarter85 7 років тому

    Not only is the maths in this really cool, but I also loved the cheeky Nail and Gear hiding in the background :)

  • @TheMrMerudin
    @TheMrMerudin 7 років тому +21

    4:30 theory of T H I C C N E S S

  • @danielrodgers3002
    @danielrodgers3002 6 років тому

    Fractal sets and the Fibonacci sequence seem to be a base geography of our world. In this video you seem to show that the Fibonacci sequence auto-magically flows out of the Mandelbrot set. Extremely fascinating, thanks.

  • @SoumilSahu
    @SoumilSahu 7 років тому +122

    Math is amazing. Who even discovers this stuff?!

    • @Cellkist
      @Cellkist 7 років тому +79

      Soumil Sahu mathematicians

    • @SoumilSahu
      @SoumilSahu 7 років тому +16

      +Cellkist obviously, but who goes out of their way to say, "today im gonna pull out the Fibonacci sequence out of a weird shape"

    • @axemenace6637
      @axemenace6637 7 років тому +36

      Soumil Sahu They don't. They explore a weird shape and say "Wow! Fibonacci sequence relates to it!"
      How do they find the weird shape to being with? Well, mathematicians make random problems up and hope they lead to something interesting. The Mandelbrot set was a lucky discovery!

    • @Pete-Prolly
      @Pete-Prolly 7 років тому +11

      Soumil Sahu sometimes it's a Mathematician, sometimes a "non- Mathematician" notices a pattern and wants to know: "does this 'thing' ever stop or does it go on forever?" They may get bored of it, or keep studying it, or even become obsessed with it (especially if their pattern appears to present itself everywhere; it's a constant reminder.)

    • @JM-us3fr
      @JM-us3fr 7 років тому +2

      People who think it's amazing

  • @rivertaig8703
    @rivertaig8703 7 років тому +1

    Mind blown! I think it's so incredibly cool how sites like Numberphile, 3 Blue 1 Brown, and Brilliant are making mathematics fun and inspirational. If you haven't checked out Brilliant's site, I highly recommend it for any curious minds.

  • @ouss
    @ouss 7 років тому +12

    she is BACK

  • @EmdrGreg
    @EmdrGreg 7 років тому +2

    Can you imagine how blown away Fibonacci would be if he could see the Mandelbrot set...

  • @MasterHigure
    @MasterHigure 7 років тому +58

    0:45 What's up with the up-arrow-paper appearing in all the videos lately? Oh, and 7:32 should be 1/2 + 1/2 = 2/4.

    • @zinnakatt8312
      @zinnakatt8312 7 років тому +3

      MasterHigure, That's funny, do more arithmetic.

    • @numberphile
      @numberphile  7 років тому +52

      Freshman Sum Freshman Sum!

    • @LastRellik
      @LastRellik 7 років тому +2

      Baaahahahahahahahahajahahahahahahajajaja

    • @MasterHigure
      @MasterHigure 7 років тому +75

      I mean, you messed up a Freshman sum. That's basically a Parker freshman sum right there.

    • @Patrick_Bard
      @Patrick_Bard 7 років тому +8

      Yeah, you said that Freshman Sum was in a certain way and showed it differently.

  • @Dyslexic-Artist-Theory-on-Time
    @Dyslexic-Artist-Theory-on-Time 7 років тому

    We also have the start of the Fibonacci numbers 0,1,1... in the complex plane. The zero in the centre can represent t=0 the moment of now in an individual reference frame. We also have negative 1 and positive 1 with a rotation 2π that is a constant represented by ħ=h/2π. Therefore we even have the start of the Fibonacci numbers 0,1,1,2,3,5,8,13,21... forming spiral on all levels of creation!

  • @Purpial
    @Purpial 6 років тому +4

    Person: "what the heck happened to your mind?!"
    Me: "oh dont worry it was just blown"

  • @davidwilkie9551
    @davidwilkie9551 10 місяців тому +1

    Fabulous presentation, thank you for the intellectual depth charge -> factual recognition time bomb of realization.

  • @russhendrix9674
    @russhendrix9674 7 років тому +45

    SHE BLINDED ME WITH SCIENCE!!

    • @GDQuaza
      @GDQuaza 5 років тому +9

      This is math, you’re even blinded by vocabulary.

    • @67PhilR
      @67PhilR 5 років тому +1

      Thomas Dolby......luv science

  • @Spongman
    @Spongman 7 років тому +1

    at 6:17, the components labeled "1/5" and "4/5" should actually be labeled "1/4" and "3/4". the "1/5" and "4/5" components are the next larger components down elephant valley.

  • @xanokothe
    @xanokothe 7 років тому +31

    Love you Dr Holly!

  • @richardfrenette6648
    @richardfrenette6648 6 років тому +1

    Love these videos. But. Is it just me, every time I watch Dr Holly Krieger, I cannot help thinking about Nicole Kidman. The resemblance, the attitude, the mysterious charm. It is as mesmerizing for me as the Mandelbrot set. Am I alone? Anyone else?

  • @aarond0623
    @aarond0623 7 років тому +7

    Because we keep going between two fractions, does the fraction approach something?

    • @Zephei
      @Zephei 7 років тому +2

      trekky0623 I believe it approaches 1 - 1/φ, where φ is the golden ratio (1 + sqrt(5))/2.

    • @Myrslokstok
      @Myrslokstok 7 років тому

      So when do we get a zoom in at the golden ratio?

    • @nasser101
      @nasser101 7 років тому

      Approaches 1

    • @alekisighl7599
      @alekisighl7599 6 років тому

      zoom in infinitely and you will get the golden ratio.

  • @rkpetry
    @rkpetry 7 років тому +1

    [04:55] Riemann's analytic continuation does something like that curve-around to get its special answers... [07:13] the ratio of Fibonacci numbers→Golden Ratio... so ask what's the sequence of numbers of each, 1 '1', 2 '3's, 4 '5's, but 7 '8's is unsymmetric, Or is it....

  • @robleytrades
    @robleytrades 7 років тому +3

    ik i dont understand what they are saying on numberphile but i still like to watch the videos

  • @navypinkdesign
    @navypinkdesign Рік тому +1

    The best Mandelbrot tour guide EVER!

  • @alejandronq645
    @alejandronq645 7 років тому +23

    Dr. Haran really makes great questions

  • @RationalDisconnect
    @RationalDisconnect 7 років тому +1

    I love how Brady has the Nail & Gear in the background.

  • @unbreakablefootage
    @unbreakablefootage 7 років тому +16

    when shits stormy outside but a new numberphile video is up

  • @Quadflash
    @Quadflash 7 років тому

    Elegant, beautiful illustration of how math describes our universe. And, how most everything is connected. Thanks for the deep sense of awe I'm feeling right no.

  • @NicosMind
    @NicosMind 7 років тому +11

    *Brady always asks some great questions.* Correct me if im wrong but his qualifications are in engineering and not math(s)? He obviously has some math skills or at the very least a good math instinct, but how good are his actual math skills? Has he done any papers and if he has has he been cited much?

    • @bengineer8
      @bengineer8 7 років тому +12

      he is a journalist

    • @NicosMind
      @NicosMind 7 років тому +1

      Bengineer8 He is but im pretty sure ive heard before that he has a qualification in engineering. And most journalists dont know anything about maths. It got me wonderin

  • @sumitmandal3901
    @sumitmandal3901 4 роки тому

    my mind is blown off right now.
    I am amazed and mesmerised
    almost ecstatic to find out the relation between Julia, Mendelbrot and Fibonacci
    Thanks a lot

  • @dmytronadtochyi9116
    @dmytronadtochyi9116 7 років тому +51

    She has one of the cutest laughs

  • @fishandchips8813
    @fishandchips8813 7 років тому +1

    seriously- you guys and this channel have had an actual, noticeable effect on my life. i am filled with awe more often than i was before folowing you. i have begub studying math in my spare time and i f*ing love it!
    i cannot thank everyone associated with this enough.

  • @RickWeberEcon
    @RickWeberEcon 7 років тому +27

    But why should the Mandelbrot set have tendrils that coincide with their Fibonacci position?! I feel like I was told I’d get an answer and all I got was an amazing new mystery

    • @angelmendez-rivera351
      @angelmendez-rivera351 4 роки тому +1

      Rick Weber Isn't that all what answers are?

    • @Scurvebeard
      @Scurvebeard 4 роки тому

      That explanation just made me more confused. The explanation seems like an even crazier way for numbers to function.

  • @toma_coffin8013
    @toma_coffin8013 2 роки тому

    I enjoy Dr Holly's videos. Brillance is when you can solve known math, Genius is when you discover/invent NEW math,

  • @scottjampa6374
    @scottjampa6374 7 років тому +14

    You had me at Fibona..wow those eyes...

  • @stickfiftyfive
    @stickfiftyfive Рік тому

    Just noticed that at 6:07, the hyperbolic component labeled as 1/5 is actually the 1/4 component and the next largest one the right is actually the 1/5 component.

  • @prophecycat5058
    @prophecycat5058 7 років тому +3

    Gotta love that 9:59

  • @theroo92
    @theroo92 7 років тому

    Dr Holly Krieger and the Mandelbrot Set, name a more iconic duo... I'll wait.

  • @akikarvonen
    @akikarvonen 7 років тому +27

    Ah, Dr. Krieger! Must be my lucky day!

  • @pierreabbat6157
    @pierreabbat6157 7 років тому

    You could draw a straight line from 1/4 to the waist. Since the map is 1/2-sqrt(1/4-z), the straight line from 1/4 is still straight in the circle. And an arc subtends half the angle from a point on the circumference that it does from the center. So the bearing of the point on the circle from 0 is the same as the bearing of the point on the cardioid from 1/4.

  • @skroot7975
    @skroot7975 7 років тому +5

    Math never ceases to amaze me.

  • @williamsquires3070
    @williamsquires3070 7 років тому

    I love mathematics because there’s so much hidden beauty and unexpected patters recur in seemingly unrelated systems. One can keep digging deeper and deeper and still find unexpected patterns that’ll keep you busy for a lifetime... if you let it! :)

  • @ElektrykFlaaj
    @ElektrykFlaaj 7 років тому +4

    I'm watching this on high, sounds awesome

  • @Vexins
    @Vexins 2 роки тому

    2:10, they found us
    Interest in fractals from those sources did cause me to pursue the higher maths and actually learn a bunch of cooler things too in college. I don’t doubt a math focused documentary on visuals would contribute to greater interest in pure math.

  • @JanSanono
    @JanSanono 7 років тому +229

    Exactly 10 minutes...
    😍 it's beautiful

    • @johnox2226
      @johnox2226 7 років тому +85

      Jan Sanono It's actually 9:59

    • @O_Chey_
      @O_Chey_ 7 років тому +25

      You are probably a physicist

    • @veralapsa
      @veralapsa 7 років тому +11

      If you take the frame count of 14975 @ 25 fps it's exactly 9:59, no .something, so John Ox is correct.

    • @Oohenry1
      @Oohenry1 7 років тому +9

      10minutes is the threshhold for more money/view

    • @wlan246
      @wlan246 7 років тому +3

      And the video isn't bad either.

  • @exiledintheus7251
    @exiledintheus7251 4 роки тому +1

    So mandelbrot set which is supposed to be the equation that eliminates the electronic interference that is heard when transmitting by wire has nothing to do with the way electricity behaves or anything to do with atomic numbers or weight.

  • @donerickson1954
    @donerickson1954 7 років тому

    I could listen/watch Dr Holly Krieger all day.

  • @shallio
    @shallio 7 років тому +4

    Hey, thanks as always

  • @elbaecc
    @elbaecc 4 роки тому +1

    I have said it before and I will say it again. Dr Holly might as well be Amy Adam's more academically inclined sister. If Dr Holly ever makes a discovery worthy of a Hollywood movie, we know who to cast in it.

  • @origamicentral4441
    @origamicentral4441 7 років тому +11

    But does 0 count as a fibonacci number?

    • @BradMcHelm
      @BradMcHelm 7 років тому +10

      By definition, the first two Fibonacci numbers are 0 and 1, and each remaining number is the sum of the previous two. Some sources omit the initial 0, instead beginning the sequence with two 1s

    • @datojokhadze7860
      @datojokhadze7860 7 років тому +3

      there are 2 definitions,one says that F1=1 F2=1,the other says that F0=0 F1=1 F2=1.But i don't think that F0 makes any impact,so it's usually omitted

    • @jony4real
      @jony4real 7 років тому +10

      In fact, there is an often-forgotten version of the Fibonacci sequence made up entirely of 0's. You start with 0 + 0 = 0, then you add the last two numbers together to get 0 + 0 = 0, then again, 0 + 0 = 0, and so on. You end up with a series (0, 0, 0, 0, 0, 0, 0, 0, 0...) that looks boring but is actually found all the time in nature. For example, once somebody ate all my cookies, so I had 0 cookies, but the weird thing is, the next day I still had 0 cookies, and then the next day 0, and then 0... cool, right? Who says maths has no application to real life?

    • @gyro5d
      @gyro5d 7 років тому

      Madder Sky; F0 = the inertial plane, before perturbation.

  • @jugglars
    @jugglars 7 років тому

    This is amazing. I'm sure that somebody can show that this connection is absolutely natural. But it definitely is not obvious and that makes it so beautiful and funny. Thumbs up!

  • @jesscarter6504
    @jesscarter6504 7 років тому +3

    Holy $^@=!!! I'm very much a humanities individual.. waited until my senior year to take college algebra, etc. I was watching this really cool show on HGTV where this treehouse expert built a treehouse for these Montessori students, and he included the Fibonacci sequence in this awesome bench he made near the reading nook up in this treehouse..I discovered that the Fibonacci sequence is ALL OVER nature etc. in the shape of leaves, etc. I discovered the Mandelbrot Set quite by accident, as, for some strange reason, I've grown really attracted to math... so that I can understand it. If the Fibonacci Sequence is all over nature... where else is it??? The exact idea of the Mandelbrot Set did NOT occur to me, but my small, feeble noodle is TOTALLY in overdrive as I watch this..Love your videos, Dr. Krieger!!

  • @aloluk
    @aloluk 6 років тому

    Wow, my mind is blown!!!!!! I had no idea where mandlebrots even came from and cant believe my favourite subject of complex numbers are hidden in them!

  • @Pacotille_6529
    @Pacotille_6529 7 років тому +18

    Nail and Gear!

  • @miksurankaviita
    @miksurankaviita 7 років тому

    Wow, this was the best video from you for a while

  • @BlacksterVFX
    @BlacksterVFX 7 років тому +4

    This was very interesting and well presented 👍🏻

  • @thetheflyinghawaiian
    @thetheflyinghawaiian 7 років тому

    I like how all these videos are done in sharpie on cardboard. It's a nice touch. Very satisfying, but I wonder how often they mess up?

  • @s0mar885
    @s0mar885 7 років тому +73

    2:40 what? i thought this was "Numberphile" and not "lets-not-get-into-that-phile"

    • @NoNameAtAll2
      @NoNameAtAll2 7 років тому +17

      s0mar
      That's Numberwang!

    • @patrickhodson8715
      @patrickhodson8715 7 років тому +8

      Because numberphile has other videos on that topic, as do other UA-cam creators. And also because it's not the topic of this video.

    • @blacxthornE
      @blacxthornE 7 років тому +15

      Yeah, this video should've totally been a 4 hour lecture.

    • @gabrielsommer2136
      @gabrielsommer2136 7 років тому +7

      It's still a channel for casual viewers. It can't replace a degree in mathematics.

  • @anteconfig5391
    @anteconfig5391 6 років тому

    The Mandelbrot set looks like it's rich with features when you zoom in on it this way 8:34 I've never seen it that way before. I just thought it looked the same way all the way down.

  • @krowwweee2918
    @krowwweee2918 7 років тому +3

    So, where is zero component?

    • @NWRIBronco6
      @NWRIBronco6 7 років тому +4

      Krowwweee presumably 0/0ths the way 'round the circle. :)

    • @FinaISpartan
      @FinaISpartan 7 років тому +1

      NWRIBronco6 0/0ths is indeterminate form. I doesn't exists as any number or exists as all numbers. I think you mean 0th way around

    • @NWRIBronco6
      @NWRIBronco6 7 років тому +2

      Final Spartan I meant what I said and I said what I meant. Trace back the rotations to 0% and you'll find your Fib value still one in the norm. So I suggest, in jest, indeterminant form. :D

    • @secularmonk5176
      @secularmonk5176 7 років тому +1

      You see where things aren't, in the Mandelbrot set? It's right there.

    • @ManuelMartinez-je1um
      @ManuelMartinez-je1um 6 років тому

      0 is not included in the fibonacci sequence