Mandelbrot Set Zoom

[human899]

this guy is a seriously cool songwriter

[19ZeldaLover95]

what program do you use to generate this? I could see making one that approximates it but this is amazing!

[jcarldeguzman]

I think I hear Music on this Video. Delete Audio on this Video.

[FlyByPC]

@jcarldeguzman The video was made specifically to go with the music. Hit mute if you don't like the audio.

[TheGodParticle]

I'm right back where i started, story of my life...

[SmexiieEmoChick]

The whole story behind this is that there was the mathematical term called the "julius" and when you solve it...you get that shape. And then you get it again and again...and again and so forth.

[FlyByPC]

@SmexiieEmoChick Good point. Specifically, the Mandelbrot Set is a "catalog" of Julia sets. The Julia sets corresponding to points inside the Mandelbrot Set are connected; those corresponding to points outside are disjoint (infinitely so, actually.)

[achozenshaman]

My friends and I are building a mandelbrot house:)

[GeirMovies]

That is a badass fucking fractal

[kridify]

We’re making a game about it! Check it out mnmgame[dot]com

[19kylegreer96]

Can anyone tell me why its the shape that it is? I'm just so confused with all this

[FlyByPC]

@19kylegreer96 Look up Mandelbrot Set. In a nutshell, the Mandelbrot Set (the black part) is the set of points for which the absolute value of the equation Z --> Z^2 + C stays at 2.0 or below when the value is calculated repeatedly. Z starts off as zero, and C is a constant, equal to the point being calculated. (Z and C are complex numbers.) For points outside the set, Z eventually becomes very large. For points in the set, Z stays small. The colors show how long the value takes to become >4.0.

[nido212]

@FlyByPC Dude, I really like your explaination of this, may I word it like that in a presentation I'm doing on Fractals? I'll give you credit and Everything.

[FlyByPC]

@nido212 No problem. Glad you found it useful.

[littlesoapfairy]

@nido212 Nise..yes you should cite it xx good look with your Presentation.....

[TechGeek95]

inception

[ThalesII]

It's mandelbrot-ception

[JR1840]

Can anyone recommend a safe website to download a mandelbrot set program?????

[FlyByPC]

@JR1840 Google for Mandelbrot Explorer (hosted on Tucows). This movie was made with an old version of UltraFractal, though.

[DarthPickley]

RIP MANDELBROT

[twilightgirl4343]

One bad ass fucking fractal

[Zap525]

a mandelbrot inside a mandlebrot.............!

[FlyByPC]

@Zap525 There are an infinite number of them. The only question is which order of infinity...

[IanTweekDP]

This song makes me wish I didn't suck at maths.

[FlyByPC]

@IanTweekDP The math isn't especially difficult. The Mandelbrot Set does require complex numbers, but they're not too hard to learn.

[2ndviolin]

@FlyByPC not hard to learn........ahahahahahaha :(

[FlyByPC]

@2ndviolin You can draw the Set with high-school algebra...

Represent each point in the plane by two numbers A and B (just like X and Y coordinates).

For each point (A, B) in the part of the plane you want to draw: Start out with three numbers: R, I, and H, all equal to zero. Do the following procedure in a loop: H = (R+I)*(R-I)+A I = 2*R*I+B R=H Keep doing this loop 100x or until R*R+I*I > 4 . Color the point according to how many times the loop ran. Repeat for each point.

[2ndviolin]

@FlyByPC thanks :)

[TheEternalForest]

my brain just melted

[MooCowMilkshakes]

My dad went to school with the doughter/son of THE Mandelbrot. :P

[hylianloach]

Jonathan Coulton? You know... Still Alive and Code Monkey?

[FlyByPC]

@hylianloach Yep. His music. It's licensed as Creative Commons; I did the video as a tribute to the song.

[kazmaslanka]

This song is absolutely wonderful - what better way to honor the aesthetics of thinking and one of the most visionary minds in current history.

[StackCityEntOfficial]

Song kind of ruins it.

[Chevemalibu1]

whoever made this must have been very bored and had plenty of time on his hands...

[DGMRuadeil]

this was a triumpf.

[temujin667]

the work of the devil!

[Xxxyzyz5698]

That's one badass fucking fractal.

[streetcornerjames]

Wasn't I doing this zoom 24 years ago?

[atomicwave]

I love mathematics, I love fractals, and I love the mandelbrot set... but seriously.. who the fuck wrote this song? Lame.

[FlyByPC]

@Niracasso The video was inspired by the song. I also did one with classical music; you might prefer that.

[Sepiantum]

How large is that image file...

[CephalopodsRock]

"one badass fucking fractal"

[17jun1989]

Remove the Song, it doesnt go with the Set.

[SilentDarkness2332]

see that space between your fingers? thats like liquefied mandelbrot..

[raunakmantri]

This one is the best mandelbroth zoom on youtube. PERIOD.

[marcmischief]

He's not still alive and teaching mathS at Yale anymore. RIP Mandelbrot

[blueapplegleek]

I did the triangle and I zoomed it so there were so many mini triangles it was so cool!

[Fulmarmusic]

61 people didn't look close enough

[Killua2001]

As far as songs about mathematicians go, I can't decide between this and Lobachevsky. It's either about a badass fucking fractal, or encouraging plagiarism, both are fun.

[StevenCHKim]

the song is hilarious

[guitarherocraze1]

Amazing. Fractal- an irregular geometrical shape forming a pattern. Zoom- magnifying something to make it look bigger.

[guitarherocraze1]

amazing fractal- an irregular geometrical shape forming a pattern

[PorcelainHearth]

pathologycal monster! D:!

[CronosYamato]

@AnonymousElektron

technically, since the Mandelbrot set is infinite, a computer can't truly represent it (nothing can actually). The fact that the set goes on forever is both fascinating and frustrating in that we can never truly draw it. This isn't saying that its a bad representation, in fact its probably very good. I'm actually an SE, so i'[d be interested in seeing your implementation. What language did you write it in?

[gedichtewiese]

gut gemacht

[mhklein57]

The song that accompanies the video is really good, but it needs some updating. Mandelbrot passed away last year. And the song would be much better without the profanity which kind of mars it.

[Killua2001]

@mhklein57

It's a song for nerds and generally anyone who knows enough mathematics to really love the song are going to be old enough to where the profanity doesn't really matter. Remember this is the same guy who gave us Re: Your Brains, he doesn't take his songs too seriously.

[punk8767]

@Killua2001 he takes his music very seriously. he thinks of himself as a musician not a comedian. which he is. he just makes a comical song every once in a while.

[streetcornerjames]

@Killua2001 I'm a nerd, this song is for the dear or hard of hearing!

[KBstreetart]

i am hating this song

[bairswan]

mindfuck



[TKTRV]

*Do Miracles Still Happen?*

^

GOOGLE> MIRACLES ARE SPACE TIME EVENTS says ONEWHITEDUCK :-)

OR > WELCOME TO THE SCOLE GHOST THEATER OF ANGELS :-)

[heatran1919]

Quite the badass fucking farctal, bro.

[Plaguedmarionette]

i love nerd rock

[kcido14]

brb head exploded

[Seedofwinter]

I find this just so fascinating. I don't understand how numbers give birth to something like that.

Song made me bust a gut. LOL

[ajaxtaur]

One bad-ass fucking fractal.

[MyNameis2long4youtub]

wait... what?! How is it still zooming in!!!

[98NinjaMexican]

what is the whole point of this

[TheS4mt]

what does this represent ?

[dannyboy12357]

@TheS4mt iterated complex functions

[shahriar98765]

The same complexity occurs in the universe..u zoom d universe, u find d galaxy Milky Way..u zoom Milky Way n find d solar system..u zoom d solar system n find d earth.....u zoom d earth n find us....u zoom us n find cells...u zoom cells n find DNA's n RNA's n so many stuffs..u zoom those stuffs n find complex molecules that makes them up...u zoom molecules n find atoms.....u zoom atoms n find protons, neutrons n electrons...u zoom them n find those particles that makes them up n goes on n on....

[AllFractUp]

Is there such a thing as the end of the Mandelbrot set? I think I found it. My example is on my you tube page.

[FlyByPC]

@AllFractUp No; it goes on forever unless you use a finite number of iterations.

[AllFractUp]

@FlyByPC

According to the dictionary I think I have found the end to the Mandelbrot set.

[FlyByPC]

@AllFractUp Well, it does have a definite "end" at "Utter West" (-2,0)...

[mickycisme]

@AllFractUp "According to the dictionary I think I have found the end to the Mandelbrot set."

Was it listed under "infinite", or "endless"?

Language is vague, the math behind the Mandelbrot set is not. The process of displaying the set specifically involves selecting a region, setting a display size, and setting an iteration limit - all three of which can be arbitrarily small or large subject to limitations like the age of the universe and how fast your computer is. Infinity never ends.

[DominoBreaker]

@FlyByPC if Mandelbrot was endless, the hole screen had to be black. and i think there are many numbers where Mandelbrot stops...

[AnonymousElektron]

@AllFractUp I wrote an implementation of the Mandelbrot set.

When you reach the limits of precision of your computer, then the pattern becomes jagged.

That doesn't mean that you've hit the bottom, you've just reached the limit of precision.

You could of course use an arbitrary precision library, but then each iteration wouldn't fit neatly into a register, and it would take much longer to do.

[CronosYamato]

@AnonymousElektron

Technically a computer couldn't make a true Mandelbrot set. Since the set is infinite, the computer couldn't truly represent it (nothing can actually). This isn't saying that its a bad representation, in fact its probably very good. I'm actually an SE, so i'[d be interested in seeing your implementation. What language did you write it in?

[CronosYamato]

@AnonymousElektron

technically, since the Mandelbrot set is infinite, a computer can't truly represent it (nothing can actually). The fact that the set goes on forever is both fascinating and frustrating in that we can never truly draw it. This isn't saying that its a bad representation, in fact its probably very good. I'm actually an SE, so i'[d be interested in seeing your implementation. What language did you write it in?

[rainislife]

I'm looking for a Mandelbrot Set that used to be here a long time ago! Can someone please send it to me if you have it???!?!? It had something referring to the universe in the title, but i'm not referring to the one that's up that is all the same vibrant color. That one was up with the one I'm looking for. ;-; someone help xD

[shrederiffic2380]

MIND = FUCKED

[TheSlyman123]

God is great

[MaZe741]

oh geeeeeez 240 p mandelbrot zoom

[FlyByPC]

@MaZe741 Times were different four years ago...

[theconverter]

There is a great BBC documentary about this! /watch?v=TTaulpClHco :D

[MrMihaly]

Really like, really, like, really really like this

I really, really (and imagitively) like this.

Oh, and the song is pretty cool too!

Thanks very much.



[discodude1402]

Why does this crazily make me think that this is how the universe works?

[Xxxyzyz5698]

Thats one badass fucking fractal.

[Knuffelaar1970]

Rest in peas

[TheBrilliantGeniuses]

but anyway. she's be telling me good girls dont have the knack for mandlebaum fractiles now do they?

[drummer1492]

So zooming into the middle of that black area wouldn't change anything or is there complexity there?

[FlyByPC]

@drummer1492 Nope; the black part is solid black. All of the complexity is at the border. Topologically, each of the colored layers is equivalent to a ring -- if you find one point at, say, 253 iterations, it is in the same band as all of the other points at that level (running around the whole set). The outer layers conform more and more to the fractal shape, like they are being vacuum-packed. There are ways of coloring the inside that do show at least some complexity, but not with this method.

[drummer1492]

@FlyByPC interesting. Thanks!

[FlyByPC]

@drummer1492 The really mind-blowing part is that there's no limit to the complexity as you zoom in. (Someone apparently proved that a while back, but I don't know the details.)

[Kittani1977]

@FlyByPC I did a fractal zoom once that, comparatively speaking, if the ending image were the size of a postage stamp the original image would have been enlarged to a surface area a trillion times the size of the visible universe.... yeah... technically at 60 fps you are "falling" to the final image at many times the speed of light at that scale. Kinda puts things in a new perspective when you look at the universe... kinda makes the universe look small.

[tgwnn]

Rest in peace :(

[birthalove22]

...one badass fucking fractal....

looks like the Buddha to me...



[trevistator]

Just so you guys know Jonathon coulton is the guy that did the still alive song for Portal andthis is just amazing

[kegmester]

I love this song :)

[shahthegreat1]

thumb print of god

[masterpanos1990]

I dont get it

[CUR50R]

NICE!

[TigerU85]

RIP Mandelbrot

[17eventeen]

Mandelbrot's in heaven, because now he's really dead

no longer still alive and teaching math at Yale

He gave us order out of chaos, he gave us hope where there was none

And a million miles away a butterfly flapped its wings

on a cold october day a man named Benoit Mandelbrot was gone.

RIP.

[Mucky1little2me3]

God bless the genius that was Madelbrot but this video is a reminder why geeks should never do music.

[KeeraJordan]

Amazing song! :-D

[KeeraJordan]

RIP, dear sir. It's beautiful.

[matleyz]

Does anyone know: is the entire Mandelbrot set contained with the area shown at the beginning, or can you find points further away from the origin? (Is the set bounded?)

[FlyByPC]

@matleyz The set is indeed bounded; if |Z| becomes greater than 2.0, the cycle increases without bound. The point in the Set farthest from the origin is "Utter West" -- (-2,0).

[lmn8nme2]

@matleyz It's like a triangle or a square, you have to start somewhere so the big one at the beginning is the start and it just keeps repeating over and over infinitely.

[mathgeek23]

This video helped so much when I learned about fractals! Thank you Dr. Mandelbrot for making my world a better place - you are missed.

[filitalian]

RIP in fractal heaven.

[joeevil]

"May he rest in a peace that's infinite at every level of magnification." - Make Magazine

[Ilusienanimations]

I wonder what Jonathan Coulton will do when he sings this live now...

[Ilusienanimations]

RIP D:

[SteelAngelJohn]

RIP.

[SirAckbar]

RIP Benoit Mandelbrot

[trr321321]

Gotta change that one line in the song: no longer alive and teaching math at Yale. RIP Benoit Mandelbrot

[cowfordflorida1]

RIP

now he's really in heaven

[MrOwn1]

what a badass fucking fractal

[ntipouan]

RIP

[welindquist]

RIP Benoit Mandelbrot. The world will one day understand your genius.

[hebesphenomegacorona]

RIP Mandelbrot

[Bertziethegreat]

RIP

[digitalArtform]

RIP B Mandelbrot

[Awakeandalive1]

Mandelbrot’s in heaven, at least he is now that he’s dead

When JoCo wrote this song he was still alive and teaching math at Yale

He gave us order out of chaos, he gave us hope where there was none

And his geometry succeeds where others fail

If you ever lose your way, a butterfly will flap its wings

From a million miles away, a little miracle will come to take you home...

[Remsoh]

RIP Benoit Mandelbrot

[tropdars]

How is this infinite complexity from a simple equation? It seems it's just infinite repetition.

[FlyByPC]

@tropdars This particular zoom is very self-similar, but if you zoom into other parts of the set, there is infinite variation / complexity. The Mandelbrot Set has been called "the most complex object in mathematics" -- and that's not far from the truth.

[Kittani1977]

@FlyByPC I once called it the DNA of The Universe. I kinda like that explanation.

[gatebuildr]

RIP Benoit Mandelbrot

[Stantzs]

Somewhere , the hypothetical chaos butterfly is crying a theoretical tear.

[CousinoMacul]

RIP Benoit Mandelbrot! He changed the world in a tiny way.

[NCKman09]

Mandelbrot's in heaven :) 2:22

[oBLACKIECHANoo]

what happend ? a random old guy that was pretty much unkown died ? mmmkay.

[FlyByPC]

@oBLACKIECHANoo Unknown to you, maybe -- but well-known to a great many mathematicians and scientists. He will be missed.

[Lagolop]

@oBLACKIECHANoo

What planet do you live on?

RIP Dr Mandelbrot. You are in fractal heaven I'm sure :)

[zankokujin]

@oBLACKIECHANoo

And more people noticed and care than will when you die.

[Beljeth]

@oBLACKIECHANoo Among mathematicians he was very well known and greatly respected.

[MtlDty]

RIP to Benoit B. Mandelbrot 20 November 1924 – 14 October 2010

And thanks for all the tripping fractals

[KellyClowers]

Goodbye Benoit Mandelbrot

[greymattersblog]

RIP Benoit Mandelbrot (1924-2010)

[PetrosWei]

RIP Benoit Mandelbrot.

[fractalzooms]

I love this fractal zoom - thankyou

[2eelShmeal]

Sorry but the song is HORRIBLE

[Zando24]

@2eelShmeal How is it horrible? It's a catchy song about math, what's not to like? lol

[jstarr23kid]

hey i once visited a website that let you do your own fractal zoom and explore a fractal pattern almost identical to wat your doin here. Can someone give me a free website that i can do that on?

[nick91210]

This song is win.

[vladissimo18]

univers is a hologram

[ChibiChii24]

Thnx for helping me with my homework.! :-)

[tetavo]

it's fun to zoom in on the very tip of the "real axis" in the mini sets. it's some of the most regular-looking stuff.

[Bicho04830]

¡Qué bello es el conjunto de Mandelbrot!

[1demonink]

people put some stupid comments about this on here. its cool. ok?

[greyface01]

Such a recursive argument about a word. If the musician was writing/singing from his heart, that why stifle that expression.

Why try to tell an artist how to do their job?

[irathesomething]

its a shape withing a shape within a shape!

[feralcat8]

Weird.... I think this song is actually describing the Julia set....

[FlyByPC]

@feralcat8 Yeah, I think that's the consensus. I think it's cool anyway, though.

[Dragonrocks]

@feralcat8

It is actually describing a Julia set. JoCo's said it before at concerts that he screwed up when he was writing the chorus.

[coolestpyro]

needs more HD

[FlyByPC]

@coolestpyro Agreed -- but that means it needs more computing time. It's on the list to do someday.

[olmen375]

I almost get religious when I watch this. Although I don't believe in a god in the normal religious sense. Awesome feeling! Stoner Magazine's thumbs up ;-)

[Destiny3231]

Mandelbrots will always fasinate me!!!

[KimiAvary]

This is way cool!

[olddirtycraig]

this has been in my favorites for years.. great tune :)

[psaile93]

ooh! my sis' boyfriend showed me this once :D was both cvreepy and awsome

[oncenefertiti]

Those are the most awesome lyrics ever written about anything. THANK YOU for the wicked Video.

[somename1235465]

how did you get the colors to repeat? Did you use some kind of fall-off curve? I do not know enough about math to figure this out.

[FlyByPC]

@somename1235465 The colors were produced by the program used to make the zoom. It seems to use a modulo color scheme, where you divide the number of iterations for each point by a certain number (say, 1000) and then use the remainder to do the color map. This way, the colors repeat every N (say, 1000) bands.

[dawinkle]

where does the color come from? its a graph right, but what determines the color?

[crazeeborg]

A spectacular representation of how beautiful math can be. Love the lyrics

[shigmiya64]

Man I have absolutely no idea what I'm looking at. Great song, though.

[onviant]

Good song except for the gratuitous profanity.

[runawaybomber]

This song rox my sox

[TheTurophile]

You could change the world in a tiny way....

[TheTurophile]

"Fractal" or "Mandelbrot Set" should be the name of a drug.

[greyface01]

@TheTurophile i nominate dmt

[ravagetalon]

LOL... Ironically. The formula described in the chorus describes a Julia Set, not a Mandelbrot Set.