Baroque Mandelbrot Zoom

[Isthecakereallyalie]

If only this looped.

[FlyByPC]

@Isthecakereallyalie Unfortunately, the mini-Mandelbrots are only nearly perfect copies.

[DJKOR420]

12 people are afraid of its simplicity

[lutubo07]

...e che finale!!

[SoshoKittycat]

I think my brain just lost its virginity.

[musicp8r]

i like it. it reminds me of string theory :)

[killerinstinct1337]

@SerenaRoberson yeah I know what you mean , kara ftw ;)

[monobrowperson]

Fractals and HAARP have much in common. Therefore, I would be very wary of them. 40,000 Japanese people would agree.

[FlyByPC]

@monobrowperson Sounds like somebody's watched "The Core" one too many times.

[DainXC]

Beautiful video. The colors and the area of the set you chose to view play along excellently with the music.

[brucelee6790]

so do all fractals contain that initial black outline

[FlyByPC]

@brucelee6790 That's just the Mandelbrot Set. A fractal is simply an object that is infinitely complex (that is, no matter how far in you zoom, it never "smooths out" and becomes simple. Check out the Wikipedia article on the Mandelbrot Set for the explanation. As for the outside, there's nothing interesting outside of the radius-2 circle centered on the origin; the initial black "lake" is all there is.

[orixaguy]

@FlyByPC

I would like to commend you for the manner in which you answered the question regarding fractals. There are others who would have taken a condescending approach with the intention of belittling the questioner. Instead, you have sparked an interest and encouraged research on the topic. A true win-win!

[FlyByPC]

@orixaguy Thanks. If asked honestly, there's no such thing as a stupid question. Nobody is born knowing about these things; we all have to start somewhere. If I can help others become interested, great!

[7teenf]

The answer is in there......somewhere

[melancholyhumour]

It's amazing how mathematics could "illustrate" the universe and it's infinity.

[thethinker372]

...I think someone slipped something into my Dr.Pepper...

[FlyByPC]

@thethinker372 That's Mr. Pibb, and it usually has that effect. Cool, no?

[Ravencliff]

R.I.P. Mandelbrot

[clubsandwedge]

Fractals are interesting to us because they somehow mirror our device of understanding, the conceptual faculty. They do this vaguely by their repetitious units. The universe isn't contained in the fractals but the mind is. All function related mathematics represents a mapping of the mind in a sense.

[killerinstinct1337]

Reminds me of Karazhan in World of Warcraft. Type Karazhan Music in search if your curious =) , very similar.

[purplefurball]

I get the shapes....but where do the colours come from???? I may be be being a bit thick here....

[FlyByPC]

@purplefurball The bands represent iteration levels (see the Wikipedia article on the Mandelbrot Set) -- the colors are chosen arbitrarily, for effect.

[PedroT2000]

@FlyByPC nice using arbitrary In the show on the set I think it was aurther c clarke that said the colors are arbitrary.

[orcodrilo]

@purplefurball There are two regions, inside and outside the set,. The colors represent how fast you get away when you start iterating from a point outside the set.

[catveezle]

@purplefurball this documentary explains it all...and contains some of the most beautiful fractal sequences ive seen anywhere.

ht tp://ww w.youtube.co m/watch?v=qB8m85p7GsU

[bittersweetxxirony]

trippy and fascinating

[wenaolong]

GOD

[alreadytaken334]

Nothing like some minor keyed harpsichord music and Mandelbrot set.

[rdrkx80]

What point does it end at?

[FlyByPC]

@rdrkx80 If you mean how far can you zoom in, it never ends -- that's what makes it so interesting.

[iwantcoolname]

@FlyByPC I would think he means what is C number for this.

[FlyByPC]

@iwantcoolname That makes sense. (-0.738716576043619213231359 + 0.16634068976336403731946 i), at 6.7418878 * 10^14 magnification.

[wenaolong]

@rdrkx80 It's kind of like pi, which is not as easy as pie, but easier to spell.

[BABOKONPRODUCTIONS]

you should make this super fast. It would definitely be mind blowing.

[FlyByPC]

Unfortunately, it would be over really quickly. Zooming past a certain point takes many hours, days, or weeks of computer time...

[iwantcoolname]

@FlyByPC that really depends on C. if you stay away from minibrots, it is much faster.

[FlyByPC]

@iwantcoolname Yes, but once it gets past the point where 32-bit (or maybe 64-bit) calculations work, it has to use arbitrary-precision math, which is many times slower. Staying away from the lakes does help -- but there is still a sharp drop in speed beyond a certain zoom point.

[denelson83]

@FlyByPC Then what we need is a new arbitrary-precision math algorithm that renders much more quickly.

[sadgreen]

nice details. these things just amaze me.

[SamSpade2010]

I think I saw my house.

[FlyByPC]

Naah -- the embedded Google Earth is at least a couple thousand times further in.

[SamSpade2010]

Silly idea. No equation could make planets and trees and houses and people. ...er....

[Mark73]

"The genetic code does not, and cannot, specify the nature and position of every capillary in the body or every neuron in the brain. What it can do is describe the underlying fractal pattern which creates them"

Yes, it's from a computer game, but it's still a great quote.

[PeeteyP]

HAHAHAHAHAHA

Was surprised that the music wasn't Bach- it works well w/ this video.

[FlyByPC]

Bach would have been good too (maybe the Little Fugue in G Minor). I may yet use that one, and/or one of the fugues from the Well-Tempered Clavier. Thanks for the comment.

[Juengerchristi]

Brilliant!

[autodidactic]

Came back to comment again: I like the big black buddha at the end. :)

[ewfq2]

Hey m8, nice video! Im making a paper about Fractals and specialising in the Mandelbrot so im into this beauty ^^ It's kinda hard though, trying to prove certain things proved impossible lol.

I had a few questions though ^^

First of all, whats the best free Fractal Viewer? (Only Mandelbrot/Julia needed to view though)

Secondly, how long would it need to compute this with a Intel Quad Processor?

Thirdly, with the program, can you create animations immediately or did u use a 2nd program for it?

[ewfq2]

Hi there, first of all great vid! Awesome shots.

I do however, have some questions:

1. Which program did you use to zoom in?

2. How much do you know about Mandelbrot/Julia fractals? (I sure could use some help on the Mandelbrot)

3. You reckon all the 'seahorses' are the same, to an extent?

[Wormlord15]

@ewfq2 the seahorses can be mapped exactly to each other after applying a transformation, so yes, they are "the same" so to speak.

[cronodob]

it's unanimous

this was wonderful

touching,not only what we see

ohhhh thank thee.

a video that was

the best fractal for, i must say..

undetecting the never...

and being in such a musical feed

5/5 a great deed indeed.

[luno44]

at the end, is that a perfect mirror flip of the initial shape? It looks like it has a slight rotation.

[goshawk0]

2:28/2:57 Great Math nerd hook to Video. Lets hope for some major big problems to emulate: with the hadron tests possibly a new 2D tool could be found.

I am no expert tHIS IS SPECULATION

??? WHERES MY SCI FI BOOK????

[k7Nick]

does this beauty ever ends...

[FlyByPC]

Fractals are infinitely complex, so no -- there is more and more detail as you continue to zoom in. Computing it does get more difficult, though, since additional precision and more iterations are needed.

[HuckleberrySlim]

this was already here, we only found it. nature is ahead of us by billions of years. lets keep playing catch up, and see if we can do as well as nature.

[mjjuna]

wow, this iterated set is very evocative of the baroque.

[Presidentjh]

Actually, Barqoue music is incredibly mathematical in nature, so it is very fitting music.

[DANVELVILL]

Wonderful.

[mf0rz]

'Seahorse Valley' -- love it!  Baroque is an awesome way of carrying it, I always considered every piece I've heard as a delivery system, message complete. I await the day I may find the time to do myself, but in the meantime request someone focus in on the 'neck' of the 'brot'. I predict great activity around the point / area where the 'head' would form a complete circle. Magnify that! there could be some vicious shit 'round them parts! ;)

[fj5a017]

amazing, that in math and in music simple concepts can generate a magnificent complexity

[alyssamcstoner]

that is some of the trippiest shit i have ever seen

[nnnwww2008]

I watched this 30 times. Great.

Is there a software package to freely zoom in and out at any position to any scale?

It would be nice to explore this universe.

[MrTad]

What tool/program do you use to zoom like this?

I have UltraFractal 4 and the zooming is not a 'smooth-zoom'; it is not flowing.

I love the Mandelbrot fractal, especially double hook at "1:49".

[poldavo]

Thanks, that was just plainly beautiful. Another reason to admire human genious.

[88sk8er88]

i can watch this for ever and never get bored

[1amzie7]

i like the music, what is it?

[banjorino]

This is so fascinating! I floating through it and it seems like I never can be able to reach something tangible:)

[raoulsghouls]

the only thing i can think of that comes close to this is facing two mirrors to each other but even that eventually turns into blackness.

[morfingaunt]

the ending is spectacular with the revisiting of the original shape.

thank you. i love the mandelbrot set and mandelbrot should be very highly commended on such a prolific discovery/invention?

[FlyByPC]

...and if you were to continue zooming, you would see an infinite series of similar "mini-lakes."

[xxwingedxx]

Except that all Mandelbrot did was fiddle around with Julia's set(aka Pheonix) which looks very similar to Mandelbrot's.

[ewfq2]

1st of all the fiddling was some nice fiddling...

2nd of all it isnt very similar to Mandelbrot... It shares similarities but thats to expected when they're so related.

[cieggou]

thanks

[cosmicskydaddy]

This is great.The music is well suited.thanks

[skymunro]

stare at it long enough feels like eating a 1/2 O of shrooms

[Muffinman10123]

Where can I get software which will plot the mandelbrot set in color and let me zoom out/in to it?

[FlyByPC]

Google for UltraFractal (or Xaos, or Fractint, or... there are many others.)

[hynesandy]

Can you imagine parachuting on a Mandelbrot planet? Don't pull the shoot too soon. Or too late!

[FlyByPC]

Hmm. That would be interesting -- except that unless you head for a lake, there's no "bottom" to the complexity...

[FractAlkemist]

Nice! I put classics to some of mine too.

[FractAlkemist]

Nice! I put some classics to mine too, although not always easy to fit.

[jdawgsworld]

ahhh...soothing music for those days i wanna go postal...love it

[powerofslack1]

wow, i was not expecting that grand finale! that was amazing.

[stormvorm]

Lurv the harpsichord music too.

[Amtiskau]

Do you have the precise coordinates in the set that were used for this?

[FlyByPC]

Yes. (-0.73871657604361899493337075 + 0.1663406897633641097956313i), at about 10^15 magnification. (It's been a while; I think the file I got those from was the right one.)

[nukemiller1]

this is beautiful. how did you program this to have these visuals. I've takin a lot of math if thats what it takes to explain.

[FlyByPC]

Basically, the design is in the complex plane (near the origin). For each point C = A+Bi in the plane, iterate Z--> Z^2+C (Z starts at 0+0i). Each point will either remain bounded (absolute value 2 or less) or it won't. If its value exceeds 2, stop and count the number of iterations used; color the point based on that number. If it stays at 2 or below for a certain number of iterations, color it black.)

[FlyByPC]

...you could always download Xaos and follow along if you want to be sure.

[nutherefurlong]

Baroque!  Good choice!

[locutio]

Thankyou, it kind of explains the universe doesn't it?

[becomethesea]

Looking at this reminds me of why I think math is beautiful.

[autodidactic]

I am very fond of harpsichords and Mandelbrots. Thank you for posting this.

[FlyByPC]

So am I -- that's why I posted it. Check out Trevor Pinnock for good harpsichord music (Rameau etc).

[yyyihad]

Que maravilla...

[btnheazy03]

You should watch this psychedelic shit when you're high.

[oemta]

How much computational time was spent to render this video?

[FlyByPC]

I forget, but I believe it was about two weeks or so on an Athlon64.

[bullet19465]

Holy fuck... the end black shape is the symmetrical opposite of the starting black shape. Mindfuck.

[prlucas1]

Aaand, if you zoom in to IT like was done to the first one, guess what you get!

[FlyByPC]

...besides a year's worth of CPU usage, since it's running on arbitrary precision math?

[prlucas1]

I mean, of course, in theory. ;)

[FlyByPC]

Check out my other Mandelbrot zoom video if you think that's cool. This one is more interesting, but the other one is a good introduction to just how complex the Mandelbrot Set is.

[sigfpe]

Actually, it's not. The M-set doesn't have exact self-symmetry and is always changing as you dive down. That makes it even more mysterious.

[MythicMediaNow]

@bullet19465 Yes it did! What the ---

[squishydoom2245]

Realize that the colors only represent how long it took for the computer generating the image to determine that point was not part of the Mandelbrot set. Black means the computer could not show that the point is not a part of the Mandelbrot set in the running time.

[nickekg]

ohhhhhh that was illuminated. also, i'm feeling some hard vertigo!

[ehjones]

If you don't find that beautiful you're brainless and soulless :-p

[abscondoindicium]

My god, it's just beautiful.

[ikmyoung]

1123143124124

[ikmyoung]

What kinds of music instruments of this music?

[FlyByPC]

It's a harpsichord; similar to a piano, except the strings are plucked instead of struck, so it's a string instrument, not (like the piano) a percussion instrument.

[gassyMaskzzz]

Are you aware if there is even a way to achieve a harpiscord without emptying the bank account in these days? I would really like to buy one.

[FlyByPC]

Well, most electronic keyboards have a "harpsichord" setting that sounds pretty good. Unfortunately, real harpsichords are generally pretty expensive. A friend of mine bought one for $100US about fifteen years ago, but that was an amazing exception. Normally, they sell for thousands of dollars, I'm told.

[ikmyoung]

harp and piano? makes great sound.. than any others.(downrightly for myself) nice music for background of big castle or something..

But it can't beat mankind voices. ^^

wish to philharmonic give me a tips of baroque musics

[DeepZoomNet]

Nice video, and great music.

I don't know about all this talk about God and the Mandelbrot set. Who was it that said, "God created the integers; all else is the work of man"?? Man, at least, has been pretty busy to get to this point.

One thing seems clear to me about the M-set...if there is intelligent alien life, past, present, or future, you can bet that eventually they will discover the same set, and be appreciating the same structures we are now...

[nisirok]

funny, God is all that I thought of as I watched this.

[ieatwiteoutforfun]

Thats not funny, its stupid.

[xxxxNothingxxxxx]

good music

[guruu29]

A lot of you seem to think complexity is evidence of god. It seems the other way around to me. If there was a god, things would be very simple. As a matter of fact, if there was a god, there would be no reason (or maybe impossible) for there to be anything other than god himself. To me this complexity is indicative of a fundamental order to the universe, one that does not require an outside creator.

[greg5566]

Wow, this video gave me chills. That was really amazing. It's so weird, "God" didn't even cross my mind watching it--why would it?

It shows the beauty of MATH nothing else. The important, really astounding thing is that math doesn't "exist," it's just a system we in some sense invented. Start with a 1. Now add 1 to it. Keep going from there, subtract, divide, etc. In no time you will end up with Mandelbrot set.

[kinnisonPaladin]

hmmm this opens up an interesting topic for conversation: math doesnt exist, and yet it does! it exists because it is merely a description of the REAL world, so in a sense math is real, but it doesnt exist because we invented it... but although you may think the Mandelbrot is simply the result of an abstract math formula, take a look around and you'll see the Mandelbrot patterns emerge in nature (google it). So maybe they do exist after all and we just happened to stumble upon them...

[RogertheLemur]

You can look at math as a map. But the map is not the terrain.

[schizophrenic123]

Or maybe there are just infinite universes, and only those with constants that allow life to come about lead to people staring about wondering why those constants just happen to be perfectly adjusted to allow life to come about.

[kinnisonPaladin]

I read somewhere that if any one of the constants of the Universe, such as the value of G, the nuclear or the electric forces in atoms, etc, were even slightly different than their actual values, then it would have been impossible for life to have existed as we know it.... that is a powerfull motive to believe in the existence of The Creator...

maybe fractals are just a testament of the beauty and infinite wisdom of His Creation..

To remind us, in times like ours, because we have forgotten..

[FlyByPC]

Of course, had those constants been different, we wouldn't have been around. So life exists only in those universes where it can exist. Feynman's multiple-universes theory makes as much sense as a Creator, to me. I haven't seen compelling evidence either way. The religious explanations I've seen don't make any sense to me, but it would be nice if there were a Creator watching out for us.

[kinnisonPaladin]

I dont know if you are right (noone does) but you are not wrong. I have thought of the same thing. But I dont think there is a way to prove Gods existence or the multiple universes theory. Maybe that is also because God made it so; to give us the free will to choose what to beleive in, and not force us to beleive in him. Maybe not. I am only giving out ideas.

Maybe, in order to acomplish our purpose in life, there HAVE to be no conclusive evidense of God, so that we keep on searching...

[Kefroth1]

All this talk of God or multiple universes are simply a means of explaining our origans. Currently, there IS NO scientific proof one way or the other and so the two ideas share one major thing in commen; they have to be taken on faith. Your personal belife one way or the other is just that. For religouse types, this is not to hard a consept. For you science only types, you got to face it... you are beliving in some one elses explaination for how we got here with out any evidence involved.

[FlyByPC]

Well stated -- except that the difference that I see between Religion and Science is that any good scientist should always be willing to accept that he or she might be wrong, when presented with compelling evidence.

Why is it that there are so many religions saying so many different things -- and not one of them is willing to say "...but we might be wrong"?

Science, to me, isn't about faith. It's about not believing anything for certain that you can't prove (and ultimately, not even that).

[barrett9h]

The problem with going 100% science is: we can't yet prove everything, and we can't prove we ever will.

Are there things that cannot be explained with science?

If you believe in such things, that's faith. That is, it's not driven by logic, but "by heart".

But if you believe science will surely explain everything, that if we can't do it now it's just because we have not advanced enough, than it's heart-based faith too.

[greg5566]

I was just going to say the same thing as FlyByPC--don't you see that the "chances" of certain conditions is utterly pointless, because there's nothing special about our circumstances, it's just the ones we live in?

It's no different than saying, "Gosh, glad Mom and Dad were at the same bar that night--there must be a God!" No, you wouldn't be wondering about it otherwise.

People would be shocked if the lottery numbers came up 1,2,3,4,5,6. But that's no more unlikely than 1,23,4,54,7,12. See?

[frameses]

But everything is set for perfect conditions. To ignore it would be what's pointless. At the level of subatomic particles everything is probabilistic, yet everything functions perfectly. There are many elements of physics, that if tweaked even 1,000th of a millionth of a millionth, the universe could not exist. If you're going to say perhaps there's an infinite number of universes and hours just happens to be one that works perfectly-that might be something, but I'll still wonder what created it

[barrett9h]

*This* universe would not exist, but parhaps another one could.

Like in Asimov's book "The Gods Themselves".

[guruu29]

not to mention that the more physics learns, the more we realize that the state of the universe is not left up to as much chance as we would think. Inflation already explains many of these "why is the universe like this" questions. As we learn more, and perhaps with a unified theory, I don't think it's unreasonable at all to think that we may one day understand why the constants in the universe HAD to be the way they are. In the mean time, the anthropic principle explains things nicely.

[Klappro]

my fried once commented, that if we zoomed in far enough, we would fine an accounting text book... GENIUS

[finnchick1]

Just because you don't need a 'god' doesn't mean that a higher being is involved. How can a human create & draw 'infinity'? That's why computers are involved. If 'god' didn't create the actual pattern, is it so hard to believe that he created the formula for us to find the pattern? If man is handed treasure, he doesn't appreciate it, but if he finds it through clues and work, then he'll appreciate it much more. That's my theory.

[Zycyzyx]

Gorgeous video. I love how it ends with the reemergence of the full set... that image combined with the winding down of the music gave me chills. :)

It's like you've voyaged as deep as you can into the universe only to find it again, within itself. The music ends just as you begin to realize what this means... it's as though the musician were saying "Now that you understand, the lesson is over."

[kinnisonPaladin]

I thought the same thing. "Man cannot understand the nature of God." Just like how he cannot comprehend how anything could calculate infinity.

[Danni4815162342]

I feel fractals represent our universe, and thats why we find them so interesting.

Apparently they are produced with a fairly simply mathematical equation.

This in turn is the main goal of science today in understanding our universe, and to finding this equation, the so called "theory of everything".

[mf0rz]

DNA is god's fingerprint... the mandelbrot it just the framework :D

[johnbourbon]

thanks for making me feel crazy.

[FlyByPC]

Welcome to the club! 8-)

[bluesfool719]

the mendelbrot set is god's finger print!!!

it is the formula for every thing.

somewere deep in the set is the earth and every thing we know

[FlyByPC]

A friend of mine once commented that he thought that if we zoomed in far enough, on the right spot, we'd find Michelangelo's decoration of the Sistine Chapel. (Personally, I think he might be right.)

[mendelbot]

Ah yes, but to what lengths are you willing to go? You may be able to find god if you look deep enough, but the devil is in the distances, as 'twere.

[refine7]

I am an atheist but as I first saw the depth of a madelbrot set I had to think of god to. No human could ever create something like that. I feel crazy too now ;)

[johnnyk2112]

You dont need god to have this complexity. It comes from the repetition of very simple number formulas, repeated over and over and over. All this complexity is the result of a very natural, ignorant, simple yet fruitful process. No god needed.

[yonirules]

thanks you for having a wonderful video, and actually taking the time to answer your comments! more people should be like this

[FlyByPC]

Thanks.

[TheCommenter7]

is there any way to get to the end?

[FlyByPC]

There is no end -- that's the fun part!

[NZblind]

Sweet zoom!

[FlyByPC]

Thanks!

[FractAlkemist]

Nice one FlyBy! And what is the tune? I'm into classics especially Baroque style and I don't know that one.

[FlyByPC]

"La Villageoise" by Rameau, played by Trevor Pinnock. It seemed appropriate.

[DrNine]

The most beautiful fractal I've ever seen. To me - it was also an artistic study in the concept of FOREVER... I think this magnificent mandlebrot fractel presentation - is what forever really looks like ... more on ... thanx for sharin' this.

[Shadow101Dancer]

excellent

[msndokaralho]

Wath's the 'logic' of the Mandelbrot fractal? Why that start shape?

[FlyByPC]

For each point, a single equation (z(n+1) = z(n)^2+C) is iterated until it can be shown to either get really large, or stay small. The colors show how long each point takes to "escape." Check out the Mandelbrot Set article at WikiPedia.

[aleprechaun]

Amazing place to end it! Nice music too.

[FlyByPC]

Thanks. When I saw that sequence, I had to do a zoom -- it was just too cool!

[sisijaekeddy]

love it

cant get enough of those fractal zooms.

[iutiubfed]

this is the best video of mandelbrot on youtube i think. the music is wonderful: so mysterious!!

[FlyByPC]

Thanks. The music is "La Villageoise" by Rameau, played by Trevor Pinnock. It's available at Magnatune dot com.

[futahroid]

a very nice animation flybypc, well done

goes well with "white rabbit" by "jefferson airplane"

regards

[FlyByPC]

It would probably go well with "A Whiter Shade of Pale," too. 8-)

[superwoofer2007]

NOOOOOO you ruined it...put some trippy music for us stoners

[FlyByPC]

You can watch it with whatever music you want. Hit the Mute button, put on A Whiter Shade Of Pale (or whatever flavor you like) on Winamp, and enjoy!

[progress2007]

very well done! bravo!

it looks so interesting everywhere that it's hard to find actually interesting spots such as this... so fantastic how long it takes until the final target self-similar structure appears...

I remember leaving my Apple //c running for days and weeks to render black and white versions of these images with the resolution 280 * 180 pixels - lol

[perceptualvortex]

Cool, very fitting music and lovely fractal.

[AndrewHawke]

That was sweet. One of the best fractal zooms I've seen here on youtube. Good choice of music too.

[smonsta]

wow. this is really great. awesome. well done