Deep zoom into Mandelbrot set

From Forgetomori: "After a trip of 10 minutes inside this Mandelbrot fractal (be sure to check the HD version on Vimeo), the original image you saw would be "billions and billions" of times larger than the whole Universe."

The final magnification is e.214. Want some perspective? a magnification of e.12 would increase the size of a particle to the same as the earths orbit! e.21 would make a particle look the same size as the milky way and e.42 would be equal to the universe. This zoom smashes all of them all away. If you were "actually" traveling into the fractal your speed would be faster than the speed of light.

You might like to know that this animation took me about two days to set up. My computer then rendered day and night non-stop for just over a month to produce the animation. The resulting twenty-eight anti-aliased 1280x720 AVI files (each just under 2GB) were each watermarked at full frames (uncompressed) Then I stitched them all together uncompressed. I also added the audio track at the same time. This was all done in Virtual dub. (except watermarking) The final watermarked Avi with audio is a whopping 46GB - Then I compressed it to 495mb so I could upload it onto vimeo. I think it still looks fairly crisp
With the compression settings adjusted to achieve the highest quality, the resulting file size was about 1.5GB and looks absolutely sweet!

Zooming into a fractal bigger than the Universe

Mark Frauenfelder is the founder of Boing Boing and the editor-in-chief of MAKE and Cool Tools. Twitter: @frauenfelder. Come and hear Mark speak at the ALA conference in Chicago on July 1.

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Bonnie

Bizarro! Bizarro! Bizarro!
Anonymous

I can’t wait for the day when techno is no longer considered futuristic. I like fractals and all but I just knew the soundtrack would be–like this.
willy359

I once wrote a Mandelbrot program in Amiga Basic. On my A500 it took 24 hours to render one full-screen frame, using only black and orange. I only ran it once. Geeky times.
eviladrian

I kind of feel like, if we could zoom in on just the right part, we’d see our own universe, packed into one of those swirls.
blackcatbonifide

I can’t watch this without Jonathan Coulton singing the Mandlebrot set song in my head:

http://www.jonathancoulton.com/songdetails/Mandelbrot%20Set
Coal

It’s not really flying into the mandlebrot “beyond the speed of light” as the perspective isn’t changing. It’s more like having a really really powerful zoom lens and looking through that while it goes from it’s extremely wide setting to extreme zoom setting. The two should not be confused, and I would love to see an actual “fly into” type.
teamfresh

very interesting comments guys! I will be taking these all into account form my next fractal production, in particular the comments about magnifying into a more detailed and complex areas rather than “Feigenbaum points” comments about the music have been noted also. Overall i am surprised at how popular this animation is. I thought most people would find it to long and boring, thankyou for all your cool comments people and I hope you all enjoy my next animation even more :)

regards

teamfresh

http://www.hd-fractals.com
t3hmadhatter

Looks like what happens when you shut your eyes and press on them. Only, this time you used an eyedropper full of food dye and LSD to make it interesting.
Agies

Needs more Jonathan Coulton.
justanotherusername

I watched this on my laptop with my face mere inches away from the screen. At the end – nice ending btw :) – the image kept moving, pulsating like a living thing. Very trippy.

Btw, on Vimeo you mention: “an extremely high quality 1.4GB version can be downloaded from my blog hd-fractals.com
I would appreciate it if it was not made into a torrent though!”

Why not?
Anonymous

Watching this while tripping on acid is the ultimate!
Anonymous

Oh boy….. mindfuck central… I just watched the hi-res video (after download for smooth playback)- coupled with the NASA ambient stream for a soundtrack… as soon as the video stopped- (I was staring at the centre of the fractal stream)- an abrubt flashback to my desktop was (is!) coupled by pronounced visual warping…. everything is zooming OUT… that was trIPPY!!
justanotherusername

Ok so I went to your website to check things out. So I suppose you want some return of investment. Fair enough I suppose. And no, I’m not a writer.
george57l

Lord Mandelbrot (the Evil One) salutes you.
dancentury

Pretty, but headache after 10 seconds.

I had one of those on my Lollapalooza t-shirt. :)
Anonymous

that was freakn cool.
I only have one wonder: what it would like if the palette stayed the same so that as Mandelbrot grows(zooming-in) the border colours would always stay as let’s say for example black and the center is always white if a gray scale was used, as far as which palette to use is up to the animator.
right now it looks like we’re zooming in, if the palette moves with the zoom my guess is it might create an effect such as the Mandelbrot is growing and as it grows it darkens or lightens or whichever depends on chosen palette.
Other than that I haven’t seen anything this badass, when i tried writing simple one myself in PHP the limit was whatever the numbers could calculate and at somepoint, the built-in numbers got so small it can’t do math anymore. My guess is your program or whatever you’re using is doing it’s own math calculations or maybe there’s a way that I haven’t ran into yet and I ddon’t know enough to build my own math calculations.
SteveT

If you zoom in just a little further, you find a ticket that reads “Inspected by no. 42″.
teamfresh

so yes there are shorter zooms that go into more interesting areas – I know. I have made some, please check out my video list on vimeo – I did not make this animation intending to break new ground, I did not realise it would end up embedded on over 50 websites and gain over 70,000 views in a few days but it did! that said my next deep zoom will be in a much more detailed area – the acid candy colours are here to stay though – its one of my trade marks ;P
GoDownMoses

Bizarro! Bizarro!
jimkirk

I’ve done similar deep zooms using Fractal eXtreme from Cygnus Software. (Years ago it was Mand2000 for the Amiga).

http://www.cygnus-software.com/index.html

Once I had my Asus eee-PC working on nothing but a zoom for 60 days straight, till we lost power. Arrrugh!
zillman

Wow, what shallow people. This totally rocks. Love the beauty of the Mandelbrot at the end. Infinite recursion.
benher

Oh great, now I’m going to spend the morning performing frightening Mandlebulb flyovers.

Oh, how I fear them! I half expect to turn around and see one floating in the corner of the room.
Anonymous

It’s pretty crazy that after creating the earth and all living things, God had enough time to put all these pretty patterns inside of all of these fractals. It probably only took him 10 minutes too… in your face Atheists! Let’s see your Dawkins do that!
- Anonymous
  
  You know it’s a mathematical function, right?
  If you’re looking for signs of a creator in fractals, you would be better off starting with trees.
dequeued

also of note, Arthur C Clarke did a documentary on Fractals awhile back, here’s a link:
http://www.youtube.com/watch?v=qB8m85p7GsU

It has a lot of fractal zooms set to progressive rock, and some amusing tech predictions from the early 90s.
They interview Mandelbrot, and some interesting computer scientists.

There’s also a delightful moment when Mr Clarke talks about how the patterns one sees in the Mandelbrot set are like the patterns one sees when they ingest psychedelic drugs, or so he was told, but he wouldn’t know anything about that…
Zaren

I watched that for about 30 seconds, starting to really appreciate the depth of what I was watching, when I suddenly got really dizzy and had to look away.
SamSam

Guys, this wasn’t funny. My graphics card cannot render a non-integer number of dimensions. You’ve gone and screwed it all up now, I think it over-heated. Every letter on the screen has a perimeter of infinite length, but only a finite volume. It makes ig realy hard to typp…
Anonymous

Thanks to Jonathan Coulton:

Mandelbrot Set youâ€™re a Rorschach Test on fire
Youâ€™re a day-glo pterodactyl
Youâ€™re a heart-shaped box of springs and wire
Youâ€™re one badass f*cking fractal
And youâ€™re just in time to save the day
Sweeping all our fears away
You can change the world in a tiny way
zikzak

As I type this, the words are shrinking in on themselves and receding.
mistersquid

That was just absolutely fucking amazing.
Grey Devil

Interesting idea, but the execution leaves much to be desired. Check http://community.electricsheep.org/ for truly beautiful fractals, this video is just too hard on the eyes because of the hard colors and simplistic fractals.
- Anonymous
  
  I guess that the main target was not to create a masterpiece, was it? To each its own, if you don’t like a particular colour scheme, it doesn’t make something “not well executed”. I really loathe people that don’t see the beauty even in a “common” Mandelbrot set just because it’s “common” and not some multi-layered Photoshop-enhanced crap.
http://www.madore.org/~david/ Ruxor

The zoom level is impressive, but zoom is always taken in a place where not much interesting happens (e.g., Feigenbaum points, which are boringly self-similar). If I can place a shameless self-plug as to what happens when you zoom (although not as deeply) in more interesting places: http://www.madore.org/~david/math/mandelbrot.html
- Anonymous
  
  Anonymous #22′s zoom although lower resolution really does pick much more interesting parts of the set. Those are beautiful.
  
  –Beryl
- SamSam
  
  @David (assuming you’re David): Those videos really are much cooler. The points are much more interesting. How do you pick them? Is there a calculation you can perform which will tell you which points will be the most interesting?
  
  Also, thanks for clearing up a misconception I had. Whenever I see zooms into the Mandelbrot set you can always tell that the zoom is heading into an obvious “edge” (not really an edge, but some point where it is clear that there is a lot of action). I always thought that the featureless expanses of plain color that you go by really were featureless expanses of plain color. At least one of your videos (#3), however, zooms into one of these plain areas, and eventually detail starts to emerge, and you start to see all the same complications. Is it the case that any arbitrarily-chosen point in the set will eventually show you interestingness? Or are there some expanses of plainess that really are plain and flat?
  
  Another question: no matter how far you zoom, you always see “holes” at every level (I’m assuming the black beetle blobs are holes). Indeed, your zooms almost always end on them. My question is: will any zoom at any arbitrarily-chosen point always reach one of these holes, eventually?
dequeued

I wrote a Mandelbrot set explorer for school, but, I could only zoom in so far before I ran out of precision, and the image would get pixelated.
Of course, the trick is to have your zoom factor be an asymptote, never approaching zero, as that would break the function, so you’re just increasing the size of the denominator.

I supposed that I could have been able to zoom in more if I used arbitrary-precision number libs, but that would have made it way too slow.
zyodei

I’ve long been fascinated with the mandelbrot set. This beautiful, exotic, infinitely fascinating shape that doesn’t exist anywhere in physical reality – and yet, has some objective existence beyond/within reality. It gobsmacks me.

I love to show it to little kids, they really get into it. Then I show them the equation that makes it – even though they don’t understand the equation, they are fascinated that it can be so concise and short.

That being said, probably the best Mandelbrot I’ve seen (and I’ve seen many) is the one that comes up when you plug in “zoom 333″ to youtube. It’s all about the palette, and the chosen point…
- Xopher
  
  I think of the Mandelbrot set as a beautiful part of nature that we couldn’t see until we developed fast computers…just as there are beauties we couldn’t see before we developed good microscopes and telescopes.
knodi

A graphic mandelbrot set was one of the first computer programs I wrote; I was so proud because all I had in the classroom was a pascal compiler, and I managed to translate a QBASIC program out of the back of a magazine into pascal and get it to draw. I also drew a sierpinski triangle, the Julia set, and another one that was all swoopy curliques.

Man, this really brings back memories. Of course, on my 486, the basic mandelbrot w/ no detail took quite a while to draw.
Rich Keller

I really, really enjoyed this. I watched it last night with my face practically pressed against the monitor and only got a little queasy. Then I watched the walls bend back and forth. Thanks for sharing it. How about late fifteenth or early sixteenth century Flemish polyphonic choral music in the background? The layers of harmony would go well with the fractal images. Josquin Despres or Ockeghem would work. And there’s always something by Bach, too, if you want something later.
otherthings

You people are playing with fire. Don’t you know the bottom of the Mandelbrot set is where the Many-Angled Ones live?
- Xopher
  
  We’re endangering our soooooooouls!
  
  Well, at least it’s not a PINK Mandelbrot set!
Anonymous

Anybody remeber “Nothing But Zooms” from http://www.artmatrix.com/?

http://www.youtube.com/watch?v=1sBdfZTl8Bg
Twyloii

dmt
Wingo

Wow, yeah. I’ll have to agree with the first two commenters. Totally awesome, but after about a minute my head started to spin.

I think if I watched that for a whole ten minutes I would probably vomit uncontrollably for a while and then wouldn’t be able to see normal for days.

That is like the brown acid.
SamSam

A nice optical illusion happens if you’ve been watching this for a few minutes and then stop it.

How do you think he chose the point to zoom into? I assume that there are many point in the Mandelbrot set that you could zoom into that look completely boring. Are there a bunch of known great points? Or can you simply pick any point on an “edge?”

I think it will only be a year or two at most before most personal computers will be able to calculate and render this on the fly, allowing a user to have this zoom into the mouse location at the same speed that this is currently running at.
- Aleknevicus
  
  “I think it will only be a year or two at most before most personal computers will be able to calculate and render this on the fly…”
  
  That seems unlikely. If it took 30 days to produce this 10 minute video using a current PC, you would need a PC that’s 4320 times faster to do it in realtime. I don’t think we’ll see such an increase in computing power in only 1 or 2 years.
teamfresh

@Coal – your right, its not really flying, and at no point did I say this was a flight. What I did say is “IF you were ‘actually’ travelling….” and that “IF” implies that you actually are not travelling…

However I do like the way you talk about the zoom lens as a way of describing the animation – I may use that in my next description. ;P

And if you would like to see an actual “fly into” type, then you should check out this animation of the recently discovered 3D Mandelbrot – aka the Mandelbulb.

http://www.hd-fractals.com/true-3d-mandelbrot/fractals/animations/810

Created using the same mathematical formula as the Mandelbrot. Some say its not the real thing, I will leave you all to make up your own mind…..
Anonymous

After watching half the video look at the Repoman ad on the right.
The lung seems to contract.
sweeet.
gollux

I’ve been swallowed by the “Total Perspective Vortex”.
kmoser

“Oh my God, it’s full of brot.”
2k

gee! I could go for some Starburst right now.
I particularly liked the way that the next iteration of the beetle was formed from the inversion of the watershed of the multiplying spines with multiplying branches on them.
I cheered out loud. col?
Anonymous

z[n+1] = z[n]^2 + c
Anonymous

It’s Mandelbrots all the way down!
damianpeterson

Somebody please build a computer that will allow me to fly through a Mandelbrot set in real time. That’s where I’d live.
Anonymous

really? no one has commented that “e.42 would be equal to the universe?”

It made me smile.

http://en.wikipedia.org/wiki/Answer_to_The_Ultimate_Question_of_Life,_the_Universe,_and_Everything#Answer_to_the_Ultimate_Question_of_Life.2C_the_Universe.2C_and_Everything_.2842.29
Anonymous

So what exactly is “bigger than the entire universe”? At what magnification? At human-eye magnification? If you zoom into matter, and then zoom into the atoms, etc…It seems that the universe itself isn’t a fixed “size.”

You need to arbitrarily assign a level of magnification to even compare, and then it’s pointless to compare another arbitrary magnification of the Mendelbrot fractal.
- Xopher
  
  I think they mean that if the final view was actual size, that would make the initial view bigger than the universe, because of the magnification. In other words, the difference in scale between anything and something e^214 times as big is larger than the difference between the size of your monitor and the size of the entire universe.
teamfresh

@samsam there are areas that are plain with no detail at all. no matter how much you magnify these areas no detail will be found, that is because these areas are “outside” of the set, as for the beetle blob holes, they are “inside” the set and there are an infinite amount of them – and they are all connected by one, and only one, infinitely thin filament that you will never ever see, but whose presence can be detected by seeing the constantly thinning bands of colour squeezing in on it from both sides.
Anonymous

Fantastic job. Mandelbrot would be proud. Just think, everything none man-made is constructed of fractals. It seemed that God thought in fractals, awesome
obeyken

Some part of my brain keeps expecting to “arrive.”
- andyhavens
  
  Yeah… I wanted an ice-cream parlor to be in the middle at the very end. Or a picture of Lady Gaga.
Bobdotcom

I watched this for about five minutes. It’s beautiful and well done. And then… I got bored. That probably says something about me that I’m not prepared to come to terms with at this time.
straponego

Meh, he didn’t go far enough. At the end there’s a picture of Jesus.

Also, regarding the rendering speed: Mandebrot lends itself very well to parallel rendering, and there are MPI implementations. Plenty of systems with 4096+ cores out there…
MrWoods

This is the reason that the iPad needs to support Flash.