The Mandelbrot Set Explained

[@TheMathemagiciansGuild]

I am now on Discord: discord.gg/q4xsmSHV (under the Maths Town name)

[@JacobRy]

Hello, is this channel still going to post?

[@vincenthabay5109]

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

[@landsurfer66]

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

[@TheMathemagiciansGuild]

Thanks for leaving such kind remarks. It's really appreciated.

[@gabenugget114]

Well done!

[@radrook7584]

You actually understood that? I salute you!

[@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!

[@x-75hurricane65]

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...

[@nicholasziglio]

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

[@mrsavedbygrace2569]

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

[@elibennett3034]

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

[@charleswiltshire]

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

[@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.

[@TheMathemagiciansGuild]

Thanks for the great feedback!

[@johnr3936]

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

[@TheMathemagiciansGuild]

Thanks John

[@willclark7314]

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.

[@rednicstone3299]

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

[@TheMathemagiciansGuild]

Thank you! And congrats on forever being comment number 1! :-)

[@stanervin6108]

🏆

[@Peterdeskater100]

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

[@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!!!

[@winkyyao1]

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

[@johneagle4384]

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

[@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.

[@mahirfr]

This was the explanation I was searching for a year.

[@TheEulex]

I see 35 "thumbs downs." This is an awesome video and I can't understand what pinhead would ever click the wrong thumb icon. Thanks for posting.

[@lagduck2209]

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!)

[@mkgamesartvisuals]

Awesome work, thank you so much for this video! Edit: Wow! I was really amazed by the fact that you've done a video about this topic but as I'm watching it completely I just have to say that the content is really well visualized and explained!!!

[@rfo3225]

Just came across this. A second viewing was required before it clicked in my brain. Thanks for an excellent presentation. I feel like I actually understand this well enough to probe further.

[@superilu]

I knew the basics of fractals and Mandelbrot, but this video takes it a step further. Thanks, I really enjoyed that!

[@blakef.8566]

This is amazing. I've never seen a visualization of this like you've done around 9:40. Thank you so much for making this video.

[@mariedamlarsen]

I absolutely love this! Thanks for the really visual explanation! I've pressed the subscribe channel, by the way 😉

[@andrewhall9492]

I really enjoyed this! Understanding makes fractals that much more enjoyable!

[@stitzelmichael]

this is exactly what i was looking for, thank yiou for the great explanation, kooking forward to the next one

[@jfr644]

This really gives a short answer to the "how" question, but not to the "why". It seems to be quite philosophical though

[@lythmashni2657]

This is definitely the best Mandelbrot video out there. please make more :)

[@stanervin6108]

I'm in! Subscriber #92! Woot Woot! Top 100 list! 💯

[@ArcticYetiz]

I am completely foreign to this subject, but that was reaaally interesting. I can imagine all the work required to do this video, so thank you !

[@Fraktalist]

wow, thank you so much for that video. it answered some of my very old questions about the mandelbrot set! thank you!!!

[@bachirblackers7299]

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

[@bartolomejkozorog3387]

Much underrated channel. Love it!

[@gl0bal7474]

thank you for such a clear precise explanation. Im looking forward to watching more of your videos

[@ElBellacko1]

this is the best video on mandebrot set, explanation, thanks.

[@danakrull6122]

Thank you for this introduction which will help me share the beauty of mathematics with my sons in our homeschool classes. I am not gifted in math but am fascinated by these concepts (and images, of course). I hope that this will help me spark a love of numbers in our boys. :-)

[@mnada72]

Thank you, that was a great demonstration for the subject.

[@mickwilson99]

Brilliant pedagogy!

[@abundantharmony]

This is the Mandelbrot video ever!

[@johnmarchington3146]

Absolutely fascinating. Thanks for a marvellous video.

[@girogiro-vh5pz]

Amazing. Very nicely explained. Thanks!

[@abhishek.chakraborty]

Thanks for making this 🙏 Looking forward to be regular subscriber if I see a fairly periodic stream of mathematics-related insightful videos 👍

[@justjay926]

You explain so very well. Thankyou 👏👏👋

[@ray017ray017]

You've made a great job to make this interesting... Or I'm just interested and I don't know why

[@Paulsinke]

Thanks this is exactly what I needed

[@NonTwinBrothers]

Awesome channel! Sent here from Maths Town

[@serma3498]

Es fascinante este mundo maravilloso en que vivimos ,las matemáticas esta en todos lados ! Maravilloso vídeo ,felicitaciones y gracias por divulgarlo

[@gavinirwin2913]

Finally something to hold my attention thank you

[@DrakenFire]

This video and the one from Numberphile really explained the Mandelbrot set. Now i get it thanks.

[@Ivan_Nano]

YES!!! Thanks for making this video! It answered all my questions. I read the Wikipedia article many times but I needed this to finish my understanding of it. The Mandelbrot set makes me feel this depth within myself that I can’t explain. It feels like god shows itself more clearly in it.

[@naringrass]

this set maps the perceivable reality, I don't know why nor how, I will find out but also will probably pass away before I finish.

[@Marcel.66]

This is explained great! Thank you

[@sigriit7886]

Very interesting and relaxing

[@trimmim]

insanly good video. tysm

[@MichaelZP1]

Mandelbrot hero!, thank you.

[@skybridg5705]

Start at 1 keep going. It never ends.

[@bergarteric5713]

Mister thanks for your explications !!! realy thanks . now i understand more this fantastic and indcredible thing of Fractale and the genious of Master Mandelbroot . Sorry for my English !!! Eric from France ..

[@GabrielsEpicLifeofGoals]

The amount of numbers it maps to is the amount of branches the bulb has, and it doublss every smaller bulb.

[@hamzahamxa5951]

Thank you for this great production

[@mikedaniels3009]

I love the calm voice and the peaceful ambiance of this presentation. So happy you subtracted the music from the presentation. I have a question though: my enigma remains Benoît's paradigmA. WHY is the equation "supposed" to stay small? WHAT was Benoît's big idea to even come up with the equation ? Much obliged in advance for bearing with a mathematical oaf.

[@tictacX1]

Great video, thank you!

[@shable1436]

Nice vid, you can't break it down much more easier than that.

[@danielduerst5067]

Thanks man for the explanation, and mostly on the mini brots!! That's amazing!! Can you go into more detail of how to find the most mimi brots in a fly over path around the shore lines of main Mandelbrot?? Simply put... Where are the best mini brot infestations??

[@bachirblackers7299]

Yes man ! We need to know more minis coz i think the mini next to the cusp is related to 1/e correct me if i were wrong . Also we need to know how transcendental numbers behave .

[@unbearifiedbear1885]

I have a fluorescent "Thunder Egg" crystal/agate about the size of a cricket ball and the formation in the middle looks _exactly_ like the Mandelbrot Cardioid.. its *incredible* Also have a raw octohedral diamond which is fractal layers of triangles on triangles on triangles, with negative spaces which are the same, triangles in triangles.. gives an amazing insight into how these objects actually form, the visual expression of the physics and mathematics which precipitate them Fractals, Mandelbrots, Paisley, Moroccan style rug patterns.. first time I did psychedelics and closed my eyes, it all made sense! I genuinely believe this is the language of creation

[@tcf70tyrannosapiensbonsai]

Just great. Thank you!

[@Teranova]

Awesome video, thank you :)

[@jk1422]

Very good video! Thank you :)

[@pvdguitars2951]

This must be my favorite video on fractals. I found a ‘weird’ butterfly effect for the Vesica Pisces surface area coefficient (=4/6Pi - 0.5xsqrt3). Approximately 1.22836969854889… It would be neat to see its behavior as c in the Mandelbrot iteration

[@RowynOfficial]

Hi maths town!

[@ogb18gang62]

Love this video

[@BountyLPBontii]

The Mandelbrot Set isn't chaotic, it IS chaos!

[@jesseliverless9811]

Actually it's what's outside the Mandelbrot set that's chaos? Since it's unstable, whereas the M.S. is stable...

[@BountyLPBontii]

@@jesseliverless9811 Sure you can look at the unstable area just around the border, but you can also look inside thru the buddhabrot set!

[@DundG]

Chaos is a general concept of not comprehensible complexity. The Mandelbrot set is a mathematical equation following this concept (so it can't be the concept by default) , and only partly as some iterations are shown to converge to a single point.

[@BountyLPBontii]

@@DundG Chaos is literally inside the Mandelbrot, since its everything that follows a bifurcation. You should watch Veritaseums Videos regarding that to learn more. Our whole reality is just the 10^99999th iteration at some point in the chaos of the original bifurcation. Everything we know is just a emergent property of the specific area of the mandelbrot our reality exists in. Im talking about us just being the next iteration after the multiverse with black holes creating another iteration yet again.

[@DundG]

@@BountyLPBontii yeah Chaotic behavior is part of the set but so is order in its convergent and non Chaotic oszilating solutions. And that about the multiverse is something we have no proof of. It's literary just an imagination of the beyond, based on our incomplete knowledge, just as people believed the earth to be flat and has an edge because the sun and moon evidently rise up and down... People can look for clues but unless proven it stays a diversion made to entertain the curios mind and is not science

[@Dr.Pepper001]

Clear as mud.

[@rickyardo2944]

WOW! Thanks!

[@Snowflake_tv]

thank you!

[@Cheesecake-hp6od]

God’s mind is crazy. To come up with something like this is mind boggling

[@EbbtideCheque]

Watched it through and all I learned was that I'm dumb as a rock. I have no idea what any of it meant. Very pretty though. 😲🤩

[@IamKavot]

Good video. Thanks!

[@Stranger_In_The_Alps]

The B in Benoit B. Mandelbrot stands for Benoit B. Mandelbrot 😎

[@MiketheNerdRanger]

That last one was friggin terrifying

[@alexking1129]

Fantastic video

[@TheMathemagiciansGuild]

Thank you

[@girogiro-vh5pz]

Are there any tools I can use to help visualise what's going on? In particular, I am interested in playing around with seeing a tiny change in C that causes a chaotic change in the result.

[@DrewNewmanEngineer]

Fantastic explainer video! What is the application that was used to create the visualization starting at 35 seconds and ending at 55 seconds? Thanks in advance.

[@RipleySawzen]

So correct me if I am wrong, you state that all points within the set are connected. I do also believe that all points outside the set are also connected. Furthermore, if I am correct, there are absolutely no lines within the set. If you zoom in far enough on any part of the set, you WILL get the minibrot shape. Is that correct?

[@PaulSzkibik]

I'm still stumped a bit. How do I know that a complex number, that is inside of the mandelbrotset, will not eventually escape into into infinity if I iterate it an infinite ammount of time or at least a really vast ammount of time? What I mean is, if we only iterate each number on the complex plane 1x times, the mandelbrotset will look very different than if we iterate each number a million times. How do we know, that these eraticly behaving functions don't escape just one iteration after we stopped iterating? So, aren't there complex numbers, that might fall out of the mandelbrotset if we just iterate it an insane ammount of time, say tree3 ammount? And if iterate we by another insane ammount, shouldn't more points escape? If the are itereations chaotic in their behavior, how is it at all clear that something, that is considered inside the mandelbrotset couldn't eventually go into infinity? As I understand most videos about this, a high number of iterations just paint a more precise pictures of the mandelbrot set, but how do we know it doesn't "erode" it by slowly eating away at the border because each iteration of each possible complex number should theoretically find yet another Number that escapes radius 2? I'm 100% sure, that I'm misunderstand something here as I'm not a math person but I want to understand, what exactly I'm missing.

[@TheMathemagiciansGuild]

Actually, you are kind of right to be stumped, it is not at all clear. The way we calculate it, just improves the picture. For some areas we know for sure, such as the main cardioid and period 2 circle, you can prove that they are in the Mandelbrot Set. For many individual points, you can study the orbit to see if it becomes truly periodic, in this case it won't escape, and there are ideas in complex dynamics to show this (this is clearer if you look at some of the Julia visuals in later videos). For points near & on the boundary it is much harder, because the orbits can become truly chaotic.

[@PaulSzkibik]

@@TheMathemagiciansGuild thanks a lot for clearing this up! At some point, because it's just beyond me, I can accept just.. uh... believing that someone proved this already. I will check out more stuff about Julia Sets now. Again, thanks for your insight!

[@bitcoinzoomer9994]

Math always has a counterpart in reality. What in reality could a projection of finite and infinite space represent? My guess is that this is a map of the multiverse

[@sawdustwoodchips]

Very clear and concise explanation!! if I may enquire, what software are you using to show the orbits?

[@NEMES1-S]

Started ok, because I had already watched several videos attempting to explain this. By 5.25 minutes, I was completely lost again. One obvious sentence say’s….’When you do algebra’……… hmm, yes well algebra was never a strong point in my secondary school maths, same as geometry. You people who understand this subject automatically assume the viewer has a good understanding of the basic terms. I so want to understand this, so I will persevere; a quality I did not possess in my teens.

[@gabenugget114]

What if we change that exponent from 2 to 3?

[@tarrahhubbell1177]

I love math and I wish I was as smart as yall

[@platosfavoritestudent6509]

wonder how many people have had genuine mental breaks because of fractals

[@tworsfeline2302]

Where'd you get the color from? Some of those are between black & purple.

[@byugrad1024]

Is the area of the mandelbrot set known (does it approach a limiting value) or is it undefined? I would think it needs to be bounded by the area of the circle with diameter 4.

[@Nick12_45]

thx!

[@jeninaverse]

The poet and Mathematian Without Division.

[@RGJubilee]

How do I get my computer to do the Mandelbrot set?

[@DreadFox_official]

In a scene, imaginary could simply mean coefficient of infinity. You can't equate infinity much like you can't equate square root -1. Numbers beyond our reach of illustration. Eventually you will get to the point where the pixels on your screen can't illustrate it for you.

[@joy9648]

Hi, thank you so much for this video it was really great :)) Just a question though - what do you mean by some values having period of one / period of two (eg at 12:33)? Thanks!

[@IqbalHamid]

@04:11 Have you got your dx's and dy's mixed up? Surely it should be the other way around such that a = dy and b = dx in the diagram.

[@trumpetzmainia]

Pausing at 10:41, I was confused about the orbit that seemed to stay at [2] for about 10 iterations before blasting off. Correct me if I'm wrong, but have you chosen a number ever so slightly close to [-2] to start with, such that it would eventually diverge? [-2] is contained within the set, but I can see why you wouldn't want that hanging out on the screen when explaining the periodic nature of the converging values... Great stuff! Thanks!