The Mandelbrot Set Explained

We take a deep dive into the Mandelbrot Set, and try to understand what is happening under the hood. In particular we introduce the concept of orbits and their unusual behaviour. I hope by introducing such detail that you will find concepts in future videos easy to understand. This video contains many handcrafted visuals that took days code and animate, plus several hours to render them in 8k. Please subscribe!

Welcome to the channel! I'm new at making mathematical explainer videos, but I hope you get something from these videos. Feel free to leave some love or constructive feedback in the comments section. Questions are also most welcome.

In this video:
00:00 Introduction
1:51 Chaos & The Mandelbrot Set
2:40 The Equation
3:31 Looking at z squared
6:48 Mandelbrot, the real part.
15:24 Complex numbers
18:35 Full Mandelbrot Set
23:23 Mini-Mandelbrots

In this series:

Extra Visuals (No commentary):

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[landsurfer]

I believe that this is now the definitive video explanation for the Mandelbrot Set. Thanks for this great production!

[vincenthabay]

this is hands down the most crystal clear explaination i've seen on the subject. When you master a subject and you are still able to enter a novice's shoes to teach him you reach the master Yoda level of pedagogy. thanks for this video

[x-hurricane]

I'm still none the wiser but I really appreciate your style of teaching...and I still think this stuff is absolutely beautiful! Cheers from NZ...

[CalvinWiersum]

I've always been fascinated by this shape as a kid (hence the pfp), but I never fully understood its origin. Thanks for fulfilling by old wish!

[nicholasziglio]

It is rare to come across explanations as beautiful as this, absolutely wonderful work!

[mrsavedbygrace]

While I've been enjoying the Maths Town videos for about a year now, I never understood the math behind the Mandelbrot set. This video is giving me a better understanding of what's happening. I don't understand the math so much but I think I can understand the logic behind it. Great video and very helpful. Thanks

[elibennett]

I know very very little about math.i was able to follow perfectly. Thank you for expanding my mind.

[VitalSine]

Fantastic video. I really enjoyed learning about the Mandelbrot set. I like how you paced your video, it was not too fast and not too slow, with well-timed pauses. I loved the animations, they really made the Mandelbrot Set come to life. I look forward to your next videos.

[charleswiltshire]

This is the best Mandelbrot explainer video I've watched. Thanks for taking the time to create it.

[johnr]

The best video ive seen on mandelbrot yet! Incredibly informative and concise

[willclark]

I suck at math and can't tell you how much this made my day. You've completely opened my eyes and can't wait to see more. Subscribed.

[rednicstone]

Verry nice and helpful video!
I like the style of it and am looking forward for episode 2.

Nice graphics btw

[Peterdeskater]

By far the best explanation on YouTube I was able to find. Very very clear. Thank you.

[winkyyao]

The best demonstration of Mandelbrot Set on Youtube. Many details!

[johneagle]

Now, I understand how a Mandelbrot Set is generated. Thank you so much.
This is very, very, very useful and well-done video.

[bachirblackers]

Thanks . I think your favorite mini mendelbrot ( mn 25) is around the trancendental 1/e . Surprising .

[HathaYodel]

We thank you for the care and thought you put into creating this excellent and succinct exposition of all the main aspects that tease and puzzle so many people who enjoy exploring Mandelbrot Sets and yearn to understand WHY and HOW they behave like this.
The visual display of period orbits is particularly illuminating.

[lagduck]

Amazing, this was so visual and intuitive without going too obvious or too abstract! (though slightly infuriating was the moments like 4:53 where upper scale and lower scale does not match (or 1 does not go to 1), but that's just little minimal thing that is ever could be imperfect, in otherwise perfect video!)

[TheAffeMaria]

Best video on the topic thank you from the bottom of my heart for making it understandable for an absolute math novice. Such beauty!!!

[mahirfr]

This was the explanation I was searching for a year.