What's so special about the Mandelbrot Set? - Numberphile

  • Published: 18 April 2019
  • Featuring Ben Sparks discussing the Mandelbrot Set (and Julia Sets).
    More links & stuff in full description below ↓↓↓
    More videos with Ben: bit.ly/Sparks_Playlist
    Ben Sparks website: www.bensparks.co.uk
    And on Twitter: twitter.com/sparksmaths
    Holly Krieger has done a few Mandelbrot videos on Numberphile...
    The Mandelbrot Set: krclip.com/video/NGMRB4O922I/비디오.html
    63 and -7/4 are special: krclip.com/video/09JslnY7W_k/비디오.html
    Pi and the Mandelbrot Set: krclip.com/video/d0vY0CKYhPY/비디오.html
    Fibonacci Numbers hidden in the Mandelbrot Set: krclip.com/video/4LQvjSf6SSw/비디오.html
    Filled Julia Set: krclip.com/video/oCkQ7WK7vuY/비디오.html
    Ben was using Geogebra software: www.geogebra.org
    Files from this video: www.geogebra.org/m/BUVhcRSv
    He mentioned the book Chaos by James Gleick: amzn.to/2vj8ubP
    Golden Spiral T-Shirt available in the Numberphile Teespring store: teespring.com/stores/numberphile
    Numberphile is supported by the Mathematical Sciences Research Institute (MSRI): bit.ly/MSRINumberphile
    We are also supported by Science Sandbox, a Simons Foundation initiative dedicated to engaging everyone with the process of science. www.simonsfoundation.org/outreach/science-sandbox/
    And support from Math For America - www.mathforamerica.org/
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Comments • 1 089

  • Christian Randall
    Christian Randall  21 시간 전

    thumbnail out here looking like a touhou screenshot

    • akrinah
      akrinah  일 전

      Best explanation of Mandelbrot I ever witnessed. Nicely done.

      • dogan k
        dogan k  일 전

        Idea of coding that little script gives me a headache.

        • Wu Li
          Wu Li  3 일 전

          The Golden Ratio has proven to express a multidimensional equation, and not be merely random, implying a fractal recursion across vast scales. If so, the physicists believe it is a multifractal of a Fractal Dragon within a Mandelbrot pattern. The Fractal Dragon can be thought of as expressing a modified version of classical logic and physics, including Relativity, while the Mandelbrot expresses the supersymmetry of Standard Theory in quantum mechanics. Hence, the pattern of iterations you can see expresses the particle-wave duality of the mathematics themselves. Above 1, the iteration explodes to infinity and beyond, expressing very wave-like behavior, while below 1 they express more quantitative particle-like behavior. Where things get really funky, is the nonlinear temporal dynamics and nonequilibrium physics.

          • 61rmd1
            61rmd1  4 일 전

            wonderful topic. The link between Julia and Mandelbrot set is not so easy to find: in the clip is not very clear, but parameters are not only one, but two: Zo and c. Varying c for each Zo, we construct a Julia set, and Mandelbrot set tell us if this Julia set is connected or not. Please, tell me if I'm right or not. Thanks a lot

            • William Gallop
              William Gallop  5 일 전

              Made in 80's a short BASIC-program for C64 to calculate and show the Mandelbroth-set.

              • Venkatesh Babu Ponnuchamy

                Spring break or spring board use vectors and matrixes. Somewhat like a ball rolling in a cup.

                • Neeraj Bute
                  Neeraj Bute  6 일 전

                  I think this is one of the best videos of numberphile. The world needs more teachers like Ben. Thanks!

                  • walabyla
                    walabyla  7 일 전

                    i like this video alot. thank you for making it. and how sympathetic is that guy. have a nice day.

                    • Aragorn Stellar
                      Aragorn Stellar  8 일 전

                      That blow-up graphic reminds me of when I cook.

                      • labibbidabibbadum
                        labibbidabibbadum  9 일 전

                        If you want your mind blown, google 3D mandelbrot.

                        • Ian Copple
                          Ian Copple  9 일 전

                          That's a beautiful code! What language did you use? I was bored at work and wrote an RStudio code that zooms in on the Mandelbrot set, but so far it's about as efficient as driving in a nail with a golf ball.

                          • CheshireCat
                            CheshireCat  11 일 전

                            I feel like a baby watching a baby mobile. I have no Idea what's going on but I like the pretty shapes

                            • Yousif Al-Yousifi
                              Yousif Al-Yousifi  11 일 전

                              Is -1 stable? (If it jumps back and forth from -1 to 1)

                              • - RedBlazerFlame -
                                - RedBlazerFlame -  13 일 전

                                14:50 lol this guy can't stop talking about Chaos Theory 😂

                                • Josh Cohen
                                  Josh Cohen  14 일 전

                                  ive been obsessed with fractals and the mandlebrot set from the moment i saw them... my jaw was dropped this WHOLE video and i barely understand it, yet it makes so much sense! thank you thank you! i LOVE this video!

                                  • Numberphile
                                    Numberphile   14 일 전

                                    Glad you liked it.

                                    • Dominick Clementson
                                      Dominick Clementson  15 일 전

                                      What's the name of the software he's using?

                                      • Theta Kongpancake
                                        Theta Kongpancake  15 일 전

                                        Thank you O:)

                                        • Syler Gaming
                                          Syler Gaming  15 일 전

                                          How is -6 less than 1......it has a mangnitude of 6 units compared to one unit of 1

                                          • movAX13h
                                            movAX13h  16 일 전

                                            Awesome explanation. Thanks!

                                            • MrStevetmq
                                              MrStevetmq  16 일 전

                                              Can I ask, When you hit an unstable part it looks like the numbers just get really big and the only reason you don't see a nice patten is that most of the dots are off the screen. What would you see if you could zoom out so that you could see all the dots?

                                              • mimz
                                                mimz  17 일 전

                                                im writing a math ib sl ia on this if anyone knows anything please reply

                                                • Nathan Thompson
                                                  Nathan Thompson  17 일 전

                                                  they might be more connected than this visualization demonstrates. plot more point please

                                                  • TraitorVek
                                                    TraitorVek  17 일 전


                                                    • TraitorVek
                                                      TraitorVek  17 일 전


                                                      • TraitorVek
                                                        TraitorVek  17 일 전

                                                        There are No Lines in Reality - Polygon Indication

                                                        • Koyakonsta
                                                          Koyakonsta  18 일 전

                                                          UnStAbLe Stable: The Movie

                                                          • Michael Taphouse
                                                            Michael Taphouse  18 일 전

                                                            Excellent breakdown

                                                            • MrTeckno
                                                              MrTeckno  18 일 전

                                                              9:50 So gosh darn pure. ❤️

                                                              • Luis Acero
                                                                Luis Acero  19 일 전

                                                                Beautiful presentation. Thank you.

                                                                • Tobias SN
                                                                  Tobias SN  22 일 전

                                                                  Huh. I never thought it was this simple. Great job explaining it!

                                                                  • Alasdair Hicks
                                                                    Alasdair Hicks  22 일 전

                                                                    What's the software for that

                                                                    • Cam Hilton
                                                                      Cam Hilton  23 일 전

                                                                      square 49? NUP xD

                                                                      • Clive Green
                                                                        Clive Green  25 일 전

                                                                        The term “utterly fascinating” has been grossly overused, and so has lost much of its currency. But this is truly, utterly amazing stuff.

                                                                        • Laurelindo
                                                                          Laurelindo  6 일 전

                                                                          Maybe use the RWhiteGoose expression "T R U L Y R E M A R K A B L E". For best effect, pronounce it in a strong Toronto accent.

                                                                          • Carl Angel
                                                                            Carl Angel  25 일 전

                                                                            Nice, looks alike the Emiglia but you put it so nicely! lol

                                                                            • Carl Angel
                                                                              Carl Angel  25 일 전

                                                                              Oh wow, I just made a comment about this transfer on Vihart page... lol - enjoy!

                                                                              • Rob Toast
                                                                                Rob Toast  26 일 전

                                                                                It really bothered me when he said the wrong things at 1:45

                                                                                • brian montgomery
                                                                                  brian montgomery  27 일 전

                                                                                  Whether the colors are outside or inside the Mandelbrot set, the colors all have a sound frequency they originate from. What is 0ne + red?

                                                                                  • t0a0
                                                                                    t0a0  27 일 전

                                                                                    awesome video! a talented teacher you are

                                                                                    • Basse
                                                                                      Basse  27 일 전

                                                                                      13:18 What if our universe is in the shape of the Mandelbrot Set...??

                                                                                      • Andrew Crowe
                                                                                        Andrew Crowe  28 일 전

                                                                                        So anyone else notice that the points of stability are reminiscent of electron; planetary, and galactic system patterns? There might be some macro crystalline/matrix structures in there as well.

                                                                                        • jack002tuber
                                                                                          jack002tuber  개월 전

                                                                                          This concept defines numberphile. All numberphile concepts evolve from this central thing. They all want to be it.

                                                                                          • oldcowbb
                                                                                            oldcowbb  개월 전

                                                                                            reminds me of nyquist diagram i learnt in control class for some reason

                                                                                            • Ben Schulz
                                                                                              Ben Schulz  개월 전

                                                                                              Navier-Stokes blows up in 3d. It goes from stable to unstable when the flow/power increases which causes turbulence.

                                                                                              • m00ny
                                                                                                m00ny  개월 전

                                                                                                Hey @Numberphile , would it be possible to uploade the sourcecode for the Programm on github ? That would be great

                                                                                                • Reason to Rule All
                                                                                                  Reason to Rule All  개월 전

                                                                                                  I still get that shudder of Wonder at the Mandelbrot set as when I first learned of it in high school.

                                                                                                  • Jeremy Jacobs
                                                                                                    Jeremy Jacobs  개월 전

                                                                                                    Russell Crowe is a mathematician?

                                                                                                    • M Walker
                                                                                                      M Walker  개월 전

                                                                                                      It seems to me that this kind of investigation may have applications in boundary conditions. Am I right?

                                                                                                      • 눈꽃Snowflake
                                                                                                        눈꽃Snowflake  개월 전

                                                                                                        I love it. Thank you so much!

                                                                                                        • 눈꽃Snowflake
                                                                                                          눈꽃Snowflake  개월 전


                                                                                                          • rajem sanorjo
                                                                                                            rajem sanorjo  개월 전


                                                                                                            • Arash Salamati
                                                                                                              Arash Salamati  개월 전

                                                                                                              i wondered about how the colors came about for 13 years now i know this is epic thank you

                                                                                                              • Nicholas Kasovac
                                                                                                                Nicholas Kasovac  개월 전

                                                                                                                Wow - this is great! Thank you Mr. Ben Sparks. I use fractals as a metaphor in a series I created for Fathers & Infants, where I explain the iteration of the fractal is similar to ontogenetic development - there's a repeating pattern but on an enlarging or diminishing scale. THIS video is PERFECT for the series I created for Toddlers & Fathers, as it so amazingly explains a toddler's developing sense of independence as they navigate AWAY from a secure base (read: stable area) until they are past the stable zone and feel a sense of insecurity/danger (read: unstable zone). This is so awesome! Thanks so much! P.S. Have you published anything with this explanation, eg, article, book, etc? I'd like to use a citation if I present this idea in the future.....or please let me know the process to request permission for use. Thank you!

                                                                                                                • raglanheuser
                                                                                                                  raglanheuser  개월 전

                                                                                                                  this guy is my favorite. dunno why

                                                                                                                  • FreemanLegend
                                                                                                                    FreemanLegend  개월 전

                                                                                                                    Pathological monster! cried the terrified mathematician

                                                                                                                    • Diana Gwako
                                                                                                                      Diana Gwako  개월 전

                                                                                                                      what about cubic

                                                                                                                      • Hydron Nool
                                                                                                                        Hydron Nool  개월 전

                                                                                                                        mandelbrot looks like dr steve brule

                                                                                                                        • Corey Grandmaison Archive

                                                                                                                          Does this math not have applications in creating stable isotopes for new elements? Great video. Thank you for your life and your work /\

                                                                                                                          • MindField
                                                                                                                            MindField  개월 전

                                                                                                                            Realmente un video excepcional, muchas gracias

                                                                                                                            • roots M
                                                                                                                              roots M  개월 전

                                                                                                                              Have someone tried those with 3d figure using j as j square equals -i

                                                                                                                              • Mud One
                                                                                                                                Mud One  개월 전

                                                                                                                                I've always loved this but never understood it. Thanks

                                                                                                                                • Will Spencer
                                                                                                                                  Will Spencer  개월 전

                                                                                                                                  The stable star boundaries that you spoke of lead me reminiscing planet/moon orbitals..

                                                                                                                                  • Will Spencer
                                                                                                                                    Will Spencer  개월 전

                                                                                                                                    Existence is just a collection of photons interacting with moderate consciousness...

                                                                                                                                    • This is the Zodiac speaking

                                                                                                                                      Dont let this distract you from the fact this is a lowkey ad for the t-shirts on the background!

                                                                                                                                      • Dominik Skorjanc
                                                                                                                                        Dominik Skorjanc  개월 전

                                                                                                                                        0:32 "is it" 🔥

                                                                                                                                        • Komodo Entertainment
                                                                                                                                          Komodo Entertainment  개월 전

                                                                                                                                          Is there a hangout place for everyone in this comment section? This is the only place I can be excited about these things and actually share that with someone.

                                                                                                                                          • Nym 2867
                                                                                                                                            Nym 2867  개월 전

                                                                                                                                            Woah, he accidentally made a visual of infinity within finity. Cool. (I’m referring to the line graph, where the infinitely many squares of a decimal less than one but greater than zero are all shown at once)

                                                                                                                                            • Michael Marek
                                                                                                                                              Michael Marek  개월 전

                                                                                                                                              Could one use part of the Mandelbrot set to generate all prime numbers? To prove the Riemann hypothesis?

                                                                                                                                              • The Fucker
                                                                                                                                                The Fucker  개월 전

                                                                                                                                                y = n^(2x)

                                                                                                                                                • J.A. Brown
                                                                                                                                                  J.A. Brown  개월 전

                                                                                                                                                  MIND COMPLETELY AND THOROUGHLY BLOWN

                                                                                                                                                  • ncbookz.com llc
                                                                                                                                                    ncbookz.com llc  개월 전

                                                                                                                                                    In the body of Christ you are stable, outside the body is chaos. Head & Body of Christ is the fractal holographic truth in all creation. As you spiral out from Logos you see The head and His body in all things.

                                                                                                                                                    • brurhh
                                                                                                                                                      brurhh  개월 전


                                                                                                                                                      • REVMr SubG3N3
                                                                                                                                                        REVMr SubG3N3  개월 전

                                                                                                                                                        "It's like a map... It's a geography of iterative stability." Genius. And not, I am not a mathematician - at all. I understand enough for some complex ideas found in Philosophy. But that is a wonderful and philosophical perspective of one of the most beautiful achievements in Mathematics.

                                                                                                                                                        • Lordvictor3 -
                                                                                                                                                          Lordvictor3 -  개월 전

                                                                                                                                                          I study informatic in france . And for my last project of the year I did a program using c# and xaml . It was able to draw mandelbrot and Julia set with various palet of colours . It was your old video about the Mandelbrot set that inspire me to do it .

                                                                                                                                                          • Jimi02468
                                                                                                                                                            Jimi02468  개월 전

                                                                                                                                                            -Can you explain in layman's terms what this Mandelbrot set is? -"The Mandelbrot set is a geography of iterative stability on the complex plane." -ok...

                                                                                                                                                            • JZ Animates
                                                                                                                                                              JZ Animates  개월 전

                                                                                                                                                              What if you change it from x^2 to x^3 or other powers of x

                                                                                                                                                              • JZ Animates
                                                                                                                                                                JZ Animates  개월 전

                                                                                                                                                                Jimi02468 ok thanks

                                                                                                                                                                • Jimi02468
                                                                                                                                                                  Jimi02468  개월 전

                                                                                                                                                                  x^3 gives a shape similar to the original set that looks like two connected blobs. If the power is a fraction like 1/2 or 3/2 then it gives a really weird looking shape.

                                                                                                                                                                  • Albert Newton
                                                                                                                                                                    Albert Newton  개월 전

                                                                                                                                                                    what is that shape on that t-shirt behind him