So what is the Mandelbrot set anyway?

[Andrews__YT]

Did you know: the B in Benoit B Mandelbrot stands for Benoit B Mandelbrot.

[Keradurakh]

Thank you for the explaination, i always wondered how Mandelbrot worked (funny enough, the name means "almond bread" in german)

[niravelniflheim]

Zoom animations for the Mandlebrot set are fun. Infinite detail with repeating patterns; almost like a cosmic secret is being revealed.

[bryangreen]

3seconds and her voice puts me to sleep or hypnotizes me

[BleuSquid]

Another thing to look at is the relationship between the Mandelbrot set and the family of quadratic Julia sets. The Mandelbrot Set can be seen as a "map" of these Julia sets.

They share the same formula (z=z² + c), but while c in the Mandelbrot set is the starting point, in the Julia sets, the initial value for z is the starting point, and C is a constant for the entire image. Thus, each point C in the Mandelbrot maps to an entire image in the Julia. A point inside the Mandelbrot will generate a fully-connected Julia. A point outside the Mandelbrot will generate a disconnected Julia. The closer a point is to the border of the Mandelbrot, the more intricate the corresponding Julia will be.

2 special cases where the Julia set is not a fractal are: c=0, and c=-2. It's not known if there are other non-fractals.

[seawright]

The song always helped me:
🎶 Just take a point called Z in the complex plane 🎵
Let Z1 be Z squared plus c, 🎶
Let Z2 be Z1 squared plus c, 🎶
Let Z3 be Z2 squared plus c, 🎶
🎵 and so on
If the series of Zs should always stay
Close to c and never trend away..
That point is in the Mandlebrot set🎵🎶🎵

[KIASK]

One of the most straightforward explanations of the Mandelbrot set I’ve ever heard. Thanks!

[dubistverrueckt]

Said in such a soothing way. I wish you had been my math teacher 👩‍🏫💖

[leyvua]

This is so helpful and interesting. Too much that I shared it with aeronautical engineering colleagues group chat. Virtual hugz from Mexico 🇲🇽

[madbrowndog]

I didn't understand a word of that, but I feel so calm and relaxed now!

[frankconley]

Super pertinent for most people. Thank you. Explained so well.

[the_excocist]

I always smile watching your videos, You're so sweet

[charldew]

I finally get it! Thank you for a very clear and succint explanation.

[randomalbum]

Its insane how much Reese Witherspoon knows about math

[Billy_the_Greek]

I really enjoyed your guest season on Jet Lag! You were brilliant!

[summer-west]

I would redo my schooling if she was the only teacher I would have to see. So pleasant and such a gorgeous approach

[Tommidgely]

Thanks for that important detail. I never realised this.

[WereWade]

I've loved the Mandlebrot ever since learning about it in high school. Even made a calculator app to generate it. One thing for anyone wondering, to figure out if a point goes towards infinity (bails out) or not, you take the 2 numbers and get the square root of them squared and added together.
2+3i becomes sqrt(4+9). And a bail out value is determined, For the. Mandlebrot, that's usually 4. If it bails out, it's not part of the Dark Inner region

[peterlustig]

You have the energy of an happy talking about the mysterious of the universe, but because you talk about the actual math involved, that’s pretty cool

[murphybed]

I never knew that this mandelbrot pattern had to do with numbers. Thanks for teaching me I appreciate it.