How the Mandelbrot set is defined

Thanks to these viewers for their contributions to translations
Bulgarian: Martin Grozdanov
French: GiveMeChocolate, Yoyodotpy
German: Josh, dlatikay
Hebrew: Omer Tuchfeld
Hindi: rajeshwar-pandey
Spanish: Marcelo Lynch

[tordg]

My god did I struggle with finding a good colouring algorithm when generating this thing

[Necrobin]

We had to program this as our last practice module. It was fabulous to watch art made out of a few lines of code and math. We also did this with Julia sets and made a gif out of it by multiplying the function with e^ti from 0 to two pi for t!

[Random-pkcs]

I love your channel so much I try to understand as much as I can, but you have given so much interesting knowledge to an aspiring math student! You have made me believe that even I can learn higher math. thank you so much. if, by the slightest chance I become a mathematician you'll have a contribution towards that!
Keep helping people like me..

[lentencraft]

The name is so funny to me. Its litterally "almond bread" in german lol

[ashotvardanyan]

Your short videos are the best on Youtube. Thanks for being so informative yet concise. These videos almost always make me go watch the whole thing and thats a very good use case for short videos. You don’t scroll through bunch of information without a point, but get intrigued, then educated. Keep it up 🔥🔥🔥❤️

[BeErnyify]

Thank you so much!
I had heard of the mandelbrot set and its weird properties and also seen this graphic presentation, but never heard how it came to be.

Now i can begin to understand its apparent amazingness

[andrewsinclair]

The fractal nature is beautiful.When you zoom in infinitely.

[forresthopkinsa]

🎵 Pathological monsters! cried the terrified mathematician
Every one of them a splinter in my eye!
I hate the Peano Space and the Koch Curve
I fear the Cantor Ternary Set
The Sierpinski Gasket makes me wanna cry

And a million miles away
A butterfly flapped its wings
On a cold November day
A man named Benoit Mandelbrot was born

[marcusscience]

Also, the set is symmetrical across the real axis, because +i and -i are equal and opposite, on equal footing. It is impossible to distinguish a complex number from its conjugate. So, whatever a number is colored, it’s conjugate will the same.

[tathagatakarmakar]

That was a nice representation of iterative functions!

[sordidknifeparty]

Jonathan Coulton does a hilarious song about the mandelbrot set

[erickappel]

Excellent explanation!
Question: What software do you use to interactively show the calculation results?

[dhkdlhdyodyoclydtkd]

This would have been useful to me about 1 year ago when I was writing an IA on fractals and couldn't for the life of me figure out how a Mandelbrot set was defined. I had to use simpler fractals instead

[jaykensinger]

Ohmigerd this might be my favorite visual explanation yet! 🧡😁

[milankovacs]

Thank you for the explanation! Been interesting in this fractal for so long

[seymenkapkiner]

I created on of these in Python a few days ago for 1024x1024 different gridpoints in the complex plane

[johnchessant]

What does the "B" stand for in Benoit B. Mandelbrot?

[RangerGhost]

That’s right there is the shape of the entire universe.

[NegativeSpacePhoto]

I've only ever heard the term "Mandlebrot Set" in reference to it being used as a sort of trigger word for a sleeper cell/Manchurian candidate character in a movie.

American Ultra with Jesse Eisenberg I think.

[devs.]

Thanks, I've been wondering about why there are different colors in these "transcendent" equations for years. The hippies never had an answer