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

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**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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thumbnail out here looking like a touhou screenshot

Best explanation of Mandelbrot I ever witnessed. Nicely done.

Idea of coding that little script gives me a headache.

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.

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

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

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

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

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

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

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

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.

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

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

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

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!

Glad you liked it.

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

Thank you O:)

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

Awesome explanation. Thanks!

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?

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

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

Like

Maths...

There are No Lines in Reality - Polygon Indication

UnStAbLe Stable: The Movie

Excellent breakdown

9:50 So gosh darn pure. ❤️

Beautiful presentation. Thank you.

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

What's the software for that

square 49? NUP xD

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

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.

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

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

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

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

awesome video! a talented teacher you are

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

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.

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

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

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

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

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

Russell Crowe is a mathematician?

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

I love it. Thank you so much!

08:47

👏👏👏👏🔥

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

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!

this guy is my favorite. dunno why

Pathological monster! cried the terrified mathematician

what about cubic

mandelbrot looks like dr steve brule

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

Realmente un video excepcional, muchas gracias

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

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

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

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

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

0:32 "is it" 🔥

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.

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)

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

y = n^(2x)

MIND COMPLETELY AND THOROUGHLY BLOWN

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.

🗿

"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.

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 .

-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...

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

Jimi02468 ok thanks

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.

what is that shape on that t-shirt behind him