Mandelbrot Zoom Sequence

The Mandelbrot Set is one of the most famous shapes in mathematics, and, like all fractals, it contains patterns at every zoom level. Learn more in our interactive course at mathigon.org/course/fractals

[@mrRicearoni34]

thanks for not putting some annoying music behind this. just pure, beautiful math visualizations.

[@Mathigon]

Glad you like it!

[@powkaboomslash]

@@Mathigon4 years later and you still reply to comments, legendary. (positive comment)

[@shipweck6253]

Still blows me away when i see this thing. It looks so crazily natural, with all the curves and patterns, yet is completely mathematical.

[@smaurtmon]

Nature follows mathematics. Why is that?

[@danielbaronne753]

@@smaurtmon because our reality is a simulation

[@OVERCLOCKexe]

@@smaurtmon Maybe it's mathematics that follows nature, and not the other way around. Maybe mathematics is a man-made system and not an inherent part of the universe.

[@ysvgames1660]

Maybe mathematics is used to describe the natural world and its phenomena

[@the_legend_274]

same thing

[@prakhyatkethamukkala2145]

props to the camera man for going to a molecular level to film this for us.

[@Panos_986]

it's a photo not a molecule

[@emanuelg1892]

bro is asking to be wooshed @@Panos_986

[@enk335]

@@emanuelg1892be quiet

[@OubleJum]

Fun fact if the highest mandelbrot set calculated existed with each pixel equalling one atom, the observable universe would not be large enough to fit the whole set

[@ChrisNathan-mm8jo]

​@@OubleJum the universe would be like a neutron compared to the Mandelbrot set

[@CesareVesdani]

Fractal zooms are the most beautiful zooms that anyone could create.

[@Stoirelius]

I don't think you understand what you're talking about. NO ONE created this. That's the whole point. We just discovered it.

[@Aladato]

I've always loved how you can find mini mandelbrot sets all around it 0:36

[@and_ppv]

but they are ever slightly different. it never repeats itself.- although no one has said that for certain yet

[@jotarosans7540]

​@@and_ppv Yeah, good luck finding a guy who will inspect to see if they repeat

[@specialk2955]

this gave me an optical illusion and now my monitor is shrinking help

[@maryannbaguipo4208]

It can if u stare for 12 seconds- 45 minutes [blinking]

[@sambaker1045]

😂

[@ceciliastroppolo5337]

Jajajaja too good😂

[@senpaiuwuomglovemepleaseeeeeej]

Ayo

[@goaway1148]

It happened to me too lol

[@scupking]

This is how I think of the universe. Infinite zoom both in and out….

[@ApexProtector]

Yes! I feel like this helped me see what I’ve always believed

[@theseawillrise]

This is accurate.

[@aliasofanalias7448]

They're actually talking about a fractal universe

[@musicgardener2142]

at this point merely held back by the boundaries of the observable universe and the planck distance at both ends of the spectrum.

[@DemonLordGamingAC0]

I have a 165HZ monitor. And I knew this from Passmark's benchmark. When it runs the Mandlebrot the effects are LSD levels of stunning

[@robertniemeyer4079]

Go on....

[@hetfieldprophet]

I think I just hallucinated and Im completely sober

[@arturotramontini4773]

Salve a tutti. Sono pensionato da poco e mi sto divertendo a generare le immagini del mandelbrot classico. Ho notato 3 cose in questo video: 1- la profondità dello zoom mi pare vada oltre la risoluzione delle 15..16 cifre del double-floating point, è una mia sensazione. Per quel che ho sperimentato fin ora, ho visto che piu si scende in profondità , più cifre e più iterazioni sono necessarie, e di conseguenza piu tempo di calcolo. Questo mi fà pensare che il video così fluido (e bellissimo!) sia stato fatto con una sequenza di immagini, che va benissimo, intendiamoci. 2- la sfumatura delle zone limitrofe. Utilizzando semplicemente solo il valore di escape-point per definire un colore, si ottengono delle zone delimitate, per sfumarle ho trovato un video che fa vedere come fare tenendo conto del logaritmo della distanza in eccesso al raggio limite. 3- quello che non ho ancora trovato come fare (che vedo qui al minuto 0:50 , e che ho visto in qualche rara immagine): sono i ghirigori nella zona intermedia. Chissà se lo scoprirò prima di tornare a casa nel modo dei più :) Ok. In ogni caso un grazie di cuore. Ciao :) Arturo.

[@meriambra1584]

ho scaricato un' applicazione che ti fa mettere a fuoco molto bene l'insieme di Mandelbrot, ma non va così in profondità, come devo fare?

[@jls769597]

There’s a part when I first saw this in math class where I saw the Buddha. It was like an outline of his meditation 🧘 pose. I tripped so hard out loud in class when I recognised it. Also it made sense it would have a connection into the realm of math and nature at the same time. I was so excited I couldn’t stop drawing it in art class and drawing Buddha next to the fractal , a side by side, I showed my math teacher and philosophy teacher both were impressed by the similarities.

[@SacsachCCABP]

Yeah just turn it to the side and it’s a buddha

[@AA-gl1dr]

Look up BuddhaBrot!

[@amc350]

Is there a time stamp? I can’t find it.

[@beynotes868]

​@@amc350already at the first second of the video

[@vicentealdea45]

its true, i was buddha

[@mb5612]

This is really trippy.😵‍💫

[@billybreathes8088]

Beautiful

[@24TRUTH1]

Astounding!!!

[@empe2013]

Great zoom! Could you, please, give the initial central point z0=x0+i y0? Thanks!

[@Atajew]

So this is what infinity looks like...

[@brianuphoff8945]

this is one of the ways they write the software which helps to make things fly through space now, and most notably, in the future....

[@user-my9is7sw9v]

想象一下几千年后的人类在宇宙中发现宇宙结构是这样子的，而且永远没有尽头

[@ameliawarfield5637]

Amazing 🤩.

[@user-pb5oz8yq2g]

can i ask you how to do this by matlab??

[@bartontenants2241]

Are you slightly shifting the center interactively? Is there a mathematical way to choose a point that will always have activity?

[@user-bf5sc8pn8x]

Zoom out from a point, then reverse the video

[@thederpling209]

@@user-bf5sc8pn8x more likely he zoomed in by hand to a point, and then made his software zoom back in to that exact point

[@timerertim]

@@thederpling209 I am currently working on my own fractal zoom engine using perturbation theory and due to my research I can assure you, that that is indeed how such software works.

[@yazanhailat8627]

@@timerertim pog champ

[@VoidHalo]

I'm just wondering out of curiosity, how long did this take to generate the fractal and then render this video? And computer specs would be appreciate for context since a higher end computer could do it much faster. I'm just curious as to the amount of processing power required to generate a video like this. And also what program you used to generate these fractals, since different different programs will probably generate them with varying degrees of efficiency. And finally, thanks for taking the time to make and share this. Cheers, and all the best! =)

[@hexagon8899]

well on my laptop (with rtx 3050) it takes a few ms to render a single 2k image multiply that by 6300 frames is about 20 seconds factor in that better gpus exist yourself

[@molor0824]

the thing with zooming is floating point precision, so you have to use some kind of special numbers that can do extremely high precision for it to be able to zoom attempted this on compute shader in unity, after zooming for a while it reached float' maximum precision

[@VoidHalo]

@@hexagon8899 6300 seconds is only what? 5.5 minutes just off the top of my head. Most of these videos are a lot longer. Though I can't recall how long this one specifically was. Of course, that number can always be scaled up, assuming it scales linearly. Thanks for the sort of benchmark to go on. No pun intended.

[@VoidHalo]

@@molor0824 I'm vaguely familiar with CS, so I understand what a floating precision number is, but I know it's remiss to assume prior knowledge when explaining things like this. I'm not too intimately familiar with computer programming concepts though so this information was useful. You provided me some terms I can look up in more detail, like how unity handle shaders. I know the words, but not how they work. Thanks for the response!

[@hexagon8899]

@@VoidHalo you are way off, 6300 seconds is 1hr 45min. and also i was saying 6300 frames

[@Sage_the_Turt]

i noticed at the end of the video, for me, it looks like it starts to zoom back out a little. but that actually just a neat optical illusion.

[@mchotzi1686]

Oh danke! Ich hatte tatsächlich ein wenig an mir gezweifelt! 🤣😂

[@Lassie23]

i love your pfp

[@bbsonjohn]

okay after staring at the video for its full length, when I scrolled down to the comments the comments seemed to be zooming out

[@nosky2142]

Gods thumbprint

[@valeriesenger468]

Complex as the human body

[@user-fm9gn5wh1d]

How on earth do you program a computer to draw this?

[@Cl4rendon]

This is what my mind generated on my first acid trip as i closed my eyes during the trip - I wasn`t even aware of fractals before the intake....

[@user-NYNY13]

Infinity and beyond............

[@jonhprime777]

Deus é realmente o maior, eu repito, O MAIOR Gênio que já existiu. Veja essas formas infinitamente se transformando e com padrões diferentes. É maravilhoso.

[@zo5er]

The only video on KZbin feels like it is 3D, but actually 2D.

[@_sam]

chill af

[@hirakuya7732]

Thisy is so beautiful 🥰 1:16 Is my favorite part

[@Haven414]

Everything I look at starts shrinking after watching this

[@XKTMRiderX]

nice hypno session ty

[@TheLoonpolice1]

There should be a number that represents the square footage of this image wrt the original frame. Sq. Miles maybe.

[@lightp1101]

are you trying to tell me that that image is in there?

[@bretgreen5314]

Deputy Barney Fife's landlady's name was: Mrs. Mendelbright. : )

[@lukmanfarid6406]

Fractal!

[@julietteb4164]

Subhan Allah

[@colinfraser1309]

Please tell me how you coloured the images so perfectly.

[@GB_0110]

it was a program

[@colinfraser1309]

Of course it was a program. If you wrote it yourself, how did you select the colours?

[@musicgardener2142]

From my understanding the colour is a representation of stability. numberphile does explain it quite well: kzbin.info/www/bejne/fHfJpaCNiN-ao80

[@colinfraser1309]

Thank you for that. When I program the Mandelbrot set I colour using the number of iterations required before it becomes unstable. However, I don’t get the colour differences in distinct areas like he does. One area might be mostly brown tones whereas another area nearby might be mostly blue tones. When I do it, both these areas are coloured similarly. I just wondered if the programmer had another trick up his sleeve.

[@beaubanhagel3345]

confound it mandlebrot youve done it

[@at_infinitum]

El hecho de que este video esta en un libro oficial de la SEP en México, pagina 14 Multiples Lenguajes.

[@graybus]

Deeper!

[@Ben-kz2km]

Not sure if you will like what you'll find down there. Drums, drums in the deep.

[@abed6391]

That’s what she said

[@AmbrosiaDreamWeaver]

No matter how deep you go, there is always another level.

[@steadie]

thats one badass fuckin fractal!

[@SherylStotomas-rc7vf]

1 question, What's a mandelbrot?

[@NOLIKEBEGGARS24]

A mandelbrot is a potentially infinite zoom about 10^2 million light years

[@Quis3555]

I wanna see what happens when you fall in the black void whatever that dark thing was

[@childreninmybasement1]

nothing

[@Cristian-kk1zf]

Praised be the lord

[@fabioelsinora6020]

Meraviglioso , la matematica sacra si esprime in progressione nella forma e nei colori più armoniosi manifestando amore e intelligenza in un tunnel di vita e verità 💖✝️🕎💟💖

[@meriambra1584]

la matematica non è un oggetto sacro

[@margaretlasota2582]

So it is infinity

[@cbalan777]

Would it be fair to describe this as the perfect balance of chaos and order?

[@reverie4632]

Only if your description repeats itself non-dually

[@Wurfenkopf]

As a mathematician, I would require some measure of quality to define "perfection"

[@cbalan777]

@@Wurfenkopf Perfection; A lack of flaws

[@aliasofanalias7448]

Enough chaos creates order, that's chaos theory, all random sequences eventually form patterns

[@DanielBarberMusic]

Understandable question, but I don't see any chaos in this system at all. To my mind, this could be considered an illustration of "perfect" order. (and I agree with other comments here that "perfection" may well be impossible to define... as well as the word "flawed") As I see and understand the Mandlebrot Set, there is nothing random about it. It is thoroughly replicable, down to the last (sic) detail. and is defined specifically by a particular mathematical formula that regenerates the exact same results every time. So, no chaos here, although there is certainly plenty of amazement and beauty... :-)

[@nikolayrayanov2895]

Oh f***, this is so trippy!

[@haruskishy]

omg I saw it in my multiple language book

[@damianbuzon8119]

🌼

[@temanuke4612]

Never watch this while drunk

[@ramseswheels17]

This looks kinda creepy

[@Raffael-Tausend]

The same sequence as in Wikipedia! :-)

[@Sebas_makiavelico-777]

Literal estoy viendo este video por qué venía en mi libro de lenguajes xd

[@zapdog_]

if you look at the center for the whole video and then look away your vision does trippy stuff

[@thamtheanimator348]

1:09 Welcome to Julia Island!

[@paulwalker6967]

Just eternity

[@adilsonmorales351]

Thes reminds me of nathan's 1024 billion bits

[@Derek102_]

O no hermano 🤯😱

[@theloreofficiall69696]

Is it just me or is this the thing i see when i close my eyes and press them tightly

[@Spaceguy69420]

0:12 this place actually has a name: Seahorse Valley

[@blossom_wyvern]

I don’t believe in gods of any kind but this is damn close to what I think the gods would be like

[@Mischus5]

Chale esto es para mí escuela. :(

[@talytah]

Like si vienes del libro de 6 grado 🤔

[@OgMorrow28]

Idk why but Mandelbrots freak me out

[@mustafael-qaisi3992]

The camera man:😎

[@Mal_BusSpotter]

proof that the cameraman is god

[@harjyot2978]

one must imagine sisyphus happy

[@user-fw6zo5fg1k]

Quien más bienes del libro de la separación jajajajaja

[@shikaishik]

仕組みを解明したいですね

[@kiezersosay49]

Life is a fractal.

[@aliasofanalias7448]

Life is a fractal. Life is a fractal.

[@childreninmybasement1]

@@aliasofanalias7448 Life is a fractal. Life is a fractal. Life is a fractal.

[@thesadpanda_]

This is how close we can get to understand how the universe might be, just infinite in various of ways but all connected

[@whiteowl1137]

Café, Tricot e Ações

[@russellandrady]

Comment section is like going out

[@jduhaime8348]

Almond toast!

[@adnaolivia1387]

então era isso que a menina de O Mecanismo vivia assistindo

[@SpiralsEarth]

Did You Know If The Smallest Bit Of The Zoom Was The Size Of The Human The Entire Fractal Would Be Bigger Than The Universe?

[@fenjii_doodles]

all these smart math people in the comments, and then there's me like: shApEs And cOlOUrs thE lIkEs Of whIch I'vE nEvEr sEEn

[@DHv2.0]

Looks like the seated Buddha

[@Snomlixm]

It **n**ends

[@williamwehling2019]

A

[@user-nm8hj7ec7v]

Buddhism is a deen, a way of life. Namo Buddhaya

[@connorericksonmusic]

This is how I would describe God.

[@CarneDoSonhador]

"Look me in the eyes..."

[@Cdoblex]

I was just going to comment something like that XD

[@Cdoblex]

"Are you gonna stay by my side...?"

[@and_gelitan]

This scares me

[@georgejetson1923]

Feeling small and insignificant yet...?.you should.

[@ashlynluther5900]

😵‍💫😵‍💫😵‍💫

[@kidspace3955]

The odd1stout did a video about this

[@kidspace3955]

Btw

[@kidspace3955]

Pls reply

[@kidspace3955]

I mean it’s not a whole video but

[@Ayoub_Kn1ght]

سبحان الله!

[@user-ys4jk9dr3z]

Soy Oliver para los que lo vean

[@43garrett]

Straight up seen this smoking dmt

[@Life4Tuna]

Im with gavin this shit freaks me out

[@elizhernandez2552]

Felicidades encontraste un comentario en español 🥳

[@djfritz2001]

You stopped it too soon. If you carry the numbers on far enough you see gods final message to his people... . . . . It's Rick Astley performing Never Gonna Give You Up

[@robertmulgrew1223]

Hebrews 13:5 (Amplified Version)

[@ilikemyhouse15]

Soup watched this.

[@_...Lexi..._]

Ns yo vengo de un libro

[@yelitza9371]

Jijiji