The Mandelbrot Set - Numberphile 

I want her handwriting as a font.

Allegedly, when Benoit B. Mandelbrot used to be asked what the "B" in his name stood for, he would reply: _The B? It stands for Benoit B. Mandelbrot!_ Legend.

At about 2:55 she says, "1+1=2". I got that ! The rest... ? Yikes. Fascinating stuff.

Those super deep zooms of the set never get old. I especially love the zooms that don't move...they just descend. And I think, it's pretty amazing how much complexity you get in such a small number space

Math can be very beautiful... The Mandelbrot set proves this.

That presenter is very good at explaining. I love how she reiterate on the things that can be more difficult for some people.

If you turn on subtitles @5:05 to 5:06 you see "[evil giggle]" lol

I hear words, but I'm not understanding them

I think we need more Holly on Numberphile

i did a presentation on fractals last year and the mandelbrot set was my big finale. this video helped me a ton! i actually kind of understand it now, but my classmates didn't. im not the best teacher.

The next part of this video has been posted over on Numberphile2 - ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-oCkQ7WK7vuY.html

You know I suck ass at any kind of math, but for some reason I love watching these vids.

f(me)=I still don't get it.

Who knew you could mathematically calculate an LSD trip?

I feel stupid for only just understanding this. And I feel doubly stupid for knowing they're trying to dumb it down for people lik me to understand. I like the idea though, of being on the cusp between 'blowing up' and not 'blowing up'. Pretty much summarised my brain watching this.

I'm too much of an iterate to understand this...

I love when Dr. Holly does anything with Numberphile. She doesn't sound like she's droneing, but rather is excited to teach and loves that which she is teaching. She's the type of teacher I bet more people wished they had had growing up when teaching Math or other subjects. I'll never understand the teachers that don't have passion for what they are teaching.

shame on me for thinking I would understand this. I'll go back to cat videos :(

Keeping watching this particular video over the years and it's still the best Mandelbrot set explanation I've seen to date. Dr. Krieger is remarkable, and the series of Numberphile videos on Mandelbrot with Dr. Krieger are all extremely clear and interesting. Would be nice to see Dr. Krieger return to lecture us on whether the Mandelbrot set is local connected and what it means if it is.

Probably my favorite Numberphile ever. It's certainly amazing how such a simple function can lead to the most wonderful art... I've never been a fan of science fiction nor art for only just the sake. Rule fact here is so much more beautiful and amazing because it is absolutely so very honest to the core. Dr Krieger, I very much appreciate your patient explanation. Thanks!

for once a club that accepts zeros (7:40)

This is by far one of my favorite mathematics videos on RU-vid. Fantastic explanation, I will refer my students here when they want a good understandable explanation of the Mandelbrot set.

This is perhaps the most enlightened description of what the Mandelbrot set is that I've ever heard, and I've been listening to explanations for at least 25 years. Very good!

Isn't there any video from this girl outside of Mandelbrot, julia set, and -7/4? Her voice is so relaxing

It must drive her British colleagues mad that she says "zee" instead of "zed", haha. Great video as usual.

why I didn't have a teacher like her ?

Instantly thought of the song by Jonathan Coulton.

I love how piano and harp music starts when zooming the Mandelbrot heart

can we take a moment to appreciate her writing?

When I started reading the description, I thought "Famously beautiful" was describing the mathematician.

Thank you Dr. Krieger. This was so easy to follow. You made what was intimidating, friendly. You have a gift.

Yes, more, please! I've read and seen stuff on the Mandelbrot set numerous times, and I understand all about the iterative nature, yet still this video was better explaining it than any of the previous attempts.

"Mandelbrot" just means "almond-bread" in German

What's the middle name of Benoit B. Mandelbrot ? A: Benoit B. Mandelbrot

Dr Holly Krieger, fantastic explanation, great teacher! The questioning back in forth in the Numberphile videos is a great learning tool. Thanks for posting.

Thanks!, after a lifetime of loving the images that's the most I've understood them. I wish I could get an explanation with this much clarity of the IFS fractals that I'm also entranced and fascinated with.

Wow, that was such a great explanation, thank you! Algebra is my highest understanding of math and I was able to understand everything you said. I'm looking forward to seeing videos on the other sets.

Someone asked, "why is two the bound after which everything blows up?", which is a very good question. The reason becomes more intuitive if you know a few important properties of complex numbers, namely that |u*v| = |u|*|v| for all complex numbers u and v, and that |u + v| >= |u| - |v| for all complex numbers u and v. Using these two properties, consider the magnitude of a given number going through this procedure. Given that z has magnitude |z|, f(z) = z^2 + c has magnitude |f(x)| = |z^2 + c| >= |z^2| - |c| = |z|^2 - |c|. Now we can consider a function based on some |c| >2. Clearly f(0) = 0^2 + c = c, and so |f(0)| = |c| > 2. Next, f(c) = c^2 + c = c*(c+1), and so |f(c)| = |c|*|c+1|, and since |c|>2, |c+1| >=|c|-|1|>1. Therefore |f(c)|=|c|*|c+1|>|c|. Now, assume that we have done this procedure enough times to reach some arbitrary number z, such that |z| > |c| > 2. (We already know that we reach a number with this property after two steps). |f(z)| = |z^2 + c| >= |z|^2 - |c| > |z|^2 - |z| = |z|*(|z|- 1). Since |z| > 2, |z| - 1 > 1, and therefore |f(z)| > |z|*(|z| - 1) > |z|. Since this is true FOR ALL |z| > |c|, we know that |z| < |f(z)| < |f(f(z))| < |f(f(f(z)))|

Excellent explanation of the Mandelbrot set :) I cant wait to see the next video!

I love the way she underlines her words leaving space for the descenders on the letters.

I'm a fractal artist. Thank you for this post!

more digits than there are elementary particles in the universe?

Thanks so much for all your videos Brady.

I'm so happy I watched this. It makes so much sense now. Thank you!

as much as i love the maths here, i lost it when she gave me that look at 7:21

Famously beautiful, Dr Holly Krieger from MIT. Featuring the Mandelbrot Set.

This is the best video I’ve seen of this! I feel like I could actually understand this beautiful piece of math now THANK YOU 😭🙌🌟

This concept really is beautiful. Made me fall into a calm, peaceful sleep in the end. Simple and great depiction of the same !!! Thanks Holly

She looks like Jenna Marbles

Famously beautiful indeed

Not sure what is cooler, the Mandelbrot set or that neat handwriting. Amazing!

This was one of the best descriptions of the Mandelbrot set I've ever heard, Benoit would be proud, huzzah Dr Krieger.

"A little messy?" The Mandelbrot Set of complex numbers is "a little messy!" This is chaos!

Zooming into the mandlebrot set will be like exploring the world I see on psychedelics, but on the internet

I really enjoyed this video! I've been wanting a video explanation for what the Mandelbrot set is for a long time

Awesome. I have always wondered this and this was such a satisfying explanation. What's still lost on me is why that set would have such crazy fractal patters.

My mind is officially blown....I always knew about Mandelbrot sets, but I never knew the logic behind them.

So Beautiful.... The Mandelbrot Set looks awesome too XD

Excellent depiction of the concept. Very easy to follow. I came for a refresher on the topic and that's exactly what I got.

I saw these colourful images when I was a kid and just always assumed that what was behind it was some unbelievably complicated maths that I had no hope of understanding. Now having watched this video along with a little reading about complex numbers, I see that it's actually quite simple and I can now properly appreciate how interesting it is. Thanks!

Where can I find the fractal animation used in this video? I need something to compliment my marij... I mean uh, I want to uh, study math.

Oh my god, she is beautiful.

The first thing I ever downloaded from the Internet was a Mandelbrot Set generator, in 1992. I've been fascinated ever since.

Wonderful video that clearly outlines the creation of the Mandelbrot Set.

Brady, you tease! Give us more Mandelbrot Now!

I love Dr. Holly Krieger. Yup, it's true.

I promise this isn't the only thing I took away from your video, but Dr. Krieger's handwriting is lovely! It was a pleasure to watch.

I'm a math nerd and I NEVER knew this. I thought I did. Thanks for being an awesome teacher. "Famously beautiful" YOU !!!

Very beautiful hand writing. ...and mathematician ;)

SHADDUP, I KNOW I'M BEAUTIFUL.

Dr. Krieger, glad to see you're doing well for yourself. You once tutored me at UIC in remedial math courses and told me I had to be more "methodical", although it's a shot in the dark if you remember. I can write programs that multiply matrices, now. Cheers.

this fractal is so beautiful

I'm impressed. It's the first time in these videos i see "i" introduced the correct way as a number with the property of i^2 = -1 and not just the squareroot of -1 (which is incorrect)

Even though I'm not currently in school, I learn something new every day.

Best explanation I have ever seen! Thank you very much!

incredible job explaining complex math in a simple and comprehensible way!

That was some trip... I wonder when I land...

Numberphile -- Question: say I take a single number line, a one dimensional continuum of numbers, such as the x-axis of a graph. If I use complex numbers, it stands to reason that on this number line is another axis perpendicular to the x-axis at 0 for the complex parts of x -- in effect, our one-dimensional number line is two-dimensional. Say then that I take this complex x-plane and add, perpendicular to it at 0, a y-axis, so now my graph is three dimensional -- a complex x-plane and a real y-axis. If I then extend the y-axis to include the complex numbers by adding yet another axis perpendicular to the y-axis AND the complex-x plane to represent the y-axis' complex part, I now have a four-dimensional system with only two variables, x and y. Can I do equations in four-dimensional space using this system?

For someone named Dr. Kreiger, this person seems remarkably sane and competent

Absolutely excellent.

You guys should do a computerphile on how this is actually plotted programatically on the computer!

well, sure now i know what it represents, but how do i get it? for instance if i would not know how it looks like what do i need to do to find this particular structure?

Good instruction and music too. Well done. Thank you.

Thank you... this is the first time I ever understand what the Madelbrot Set is about

Beautiful handwriting.

All the examples used are on the x axis, the real axis. I'd love to see you work out a few iterations off the axis, in the imaginary domain. I dont understand that part. Really weird how primes show up so much, how does that work off the axis? Definitely one of the harder numberphile videos to grasp.

Understanding what it is makes the set even more beautiful.

Happy Birthday, Benoit B. Mandelbrot!

The first comment I see is going to be about the woman's appearance... Yep, the first comment I saw was about the woman's appearance.

where is part 2? I've been waiting for a month!

Super interesting . Please, please, please more videos about fractals!

Thank you so much for this! I have to do a project on fractals with emphasis on the Mandelbrot set and it was really confusing but this helped a looooot.

"It's the guys that don't blow up rather than once that do" - sexual tension intensifies

Fascinating :) Can anyone provide a screensaver or a program displaying the Mandelbrot set? I never thought learning math would be fun, I mean I always liked it but I can spend all day watching these videos! If they had a new video every day I'd have a phd or a degree in mathematics! :p

This video was perfect! I am glad to claim that I understood every second of it. Now I understand why you can infinitely zoom in into the Mandelbrot fractal = )

Awesime, thanks for vids like this!

she has both the brain and the beauty...

This girl again :D

Bravo Dr. Krieger that was a very nice explanation!

Thank you for this. Well explained.