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Gigapixel Tapestries & Gigadecimal Pi 215

RobotWisdom writes "The new New Yorker magazine has posted two long non-technical articles about the Chudnovsky brothers and their homebrew supercomputers. One is a 1992 article about how they calculated pi to over two billion decimal places using a $70,000 cluster with 16 nodes. The other is a brandnew piece about how they spent months creating a seamless multi-gigabyte image of a fifteenth century tapestry for New York's Metropolitan Museum of Art. Tapestries are essentially pixel-art on a non-rigid (cloth) matrix, so the manual labor of photographing it inch by inch had introduced many tiny deformations in the images, which they had to mathematically iron out. Old lo-res pix of the tapestries are on the Met's site, pix of the brothers are in the world brain."
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Gigapixel Tapestries & Gigadecimal Pi

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  • by Bradee-oh! ( 459922 ) on Monday April 04, 2005 @10:38AM (#12133648)

    • by TheRaven64 ( 641858 ) on Monday April 04, 2005 @11:03AM (#12133869) Journal
      I know this is intended at a joke, but I saw a research project at Southampton University about 5 years ago that allowed multi-gigabyte images to be viewed over the Internet. Each image was split into small tiles, and lower resolution tiles were made of each segment. The entire image could be viewed at low resolution, and the user could then zoom in to the full resolution on any given area. The intended use for this system was high resolution scanned images of paintings in art galleries.
      • I know this is intended at a joke, but I saw a research project at Southampton University about 5 years ago that allowed multi-gigabyte images to be viewed over the Internet. Each image was split into small tiles, and lower resolution tiles were made of each segment. The entire image could be viewed at low resolution, and the user could then zoom in to the full resolution on any given area.

        You mean like or

      • by Speare ( 84249 ) on Monday April 04, 2005 @11:50AM (#12134295) Homepage Journal
        I've used a Flash-based system called Zoomify [] to display higher resolution mosaics (up to 50 megapixels, myself). It works well, but since it's all based on jpegs, the tile deconstruction process can introduce more compression artifacts and a little bit of softening. It's worth the space and super-simple to install and use, in my experience.
      • I was the orginal author. It's now a GPL project on sourceforge []. Check out the javascript client demo (done by Ruven Pillay), very cool.
    • I remember NASA allowed download of their huge picture of the Earth. You had to submit an email address and wait for a response (a low-tech bandwidth management system, I suppose). I still have it lying around somewhere.
      • I realize this is now somewhat offtopic, but I was interested enough in the parent post to explore further. Indeed these images are still available. But instead of some complicated "low-tech bandwidth management system," you can link to them directly off Nasa's website

        Here [] is an 8192x4096 of Earth. Created as a mosiac with 1km square tiles with no clouds
        A version [] with clouds is also available.
        Here [] is a 30000x15000 (yah, you heard me) GIF of the entire planet's city lights at night.
        A 16394x8192 []
  • by seringen ( 670743 ) on Monday April 04, 2005 @10:40AM (#12133667)
    If you're in New York, you should definitely check out the Cloisters, where the Unicorn Tapestries are held. It's right at the Northern Tip of Manhattan. A number of my friends have gone to the Met and not seen it, thinking that it'd be there. The Cloisters is probably the most stunning collection of medieval art in America in a very beautiful setting, so you should definitely check it out!
  • Link to the multigigabyte image was not linked from the article on the front page of

    Prepare for a cataclysmic event.
  • April fools (Score:5, Funny)

    by 0x461FAB0BD7D2 ( 812236 ) on Monday April 04, 2005 @10:42AM (#12133685) Journal
    Is this another April Fools article?

    David told me that they were working with I.B.M. to design what may be the world's most powerful supercomputer. The machine, code-named C64, is being built for a United States government agency.

    I mean, I loved my C64 too, but it's no supercomputer.
  • by Speare ( 84249 ) on Monday April 04, 2005 @10:45AM (#12133711) Homepage Journal
    I was just at that museum to see the tapestries in question. I have a few high-resolution (multiple-image mosaic) photographs of the architectural elements on my Quick Pix Gallery []. I also took and stitched images of almost every tapestry in the building, but have not posted them online at this time.

    It's a fascinating structure, with excellent pieces for close inspection. I encourage anyone within a couple hours drive of Manhattan to take the trip to see these in person. It's at the north end of Manhattan at Fort Tryon Park (there's also one high-resolution picture in my gallery from the park).

  • by Anonymous Coward on Monday April 04, 2005 @10:45AM (#12133720)
    ...was breaking the tapestry's copy protection. Starting in the 14th century, nobility decreed all tapestries contain a pattern of knotting designed to prevent any scanning or printing of tapestries. By the end of the 14th century, all scanner and printer manufacturers had added this anti-tapestry copying technology into their products.
  • by amanox ( 862297 )
    I can see why one would like to calcutate Pi as far as possoble, .. but tapestries ? Spending months on a multi-gigabyte picture of a tapestrie? Geez, and it's probably not even "correct" as they had to mathematicly correct some deformation or whatever errors. Seriously, what's the point? Are they doing this "just because we can", or is there some "higher goal"?
    • Re:Why? (Score:5, Informative)

      by Speare ( 84249 ) on Monday April 04, 2005 @10:54AM (#12133798) Homepage Journal
      How about reconstruction and preservation? These tapestries are in terrible condition, compared to when they were completed in the 1400s. Any work that is done on them is done with magnifying glass, tweezers and a well-trained hand. Any reference works should be as clear and detailed as possible. They don't want it to erode any more than it already has, and they had no such detailed records of it in previous ages and conditions.
    • Sure, because preserving very old and beautiful art from decay is stupid, but, by god, I must have Pi to the 5 millionth digit. 4,999,999 digits are not enough!
    • To those who modded this troll: Just because you disagree with someone's thought does not make it a troll. I think this is a perfectly reasonable question.
    • Re:Why? (Score:5, Interesting)

      by jcupitt65 ( 68879 ) on Monday April 04, 2005 @11:30AM (#12134100)
      You can do very cool stuff with a good picture of the back of a tapestry.

      The colours in tapestries are usually vegetable dyes and they fade very badly with exposure to light. If you go around a museum, the tapestries almost always look dingy and you need to use a lot of imagination to try to picture how they might have originally looked.

      However the back of the tapestry has been kept in the dark and the colours there are still dazzling. So ... if you have a good picture of the front and the back and you can resample the back image to get it to line up with the front to within a knot size, you can use the back colour to "re-tint" the front image and get an excellent visualisation of how the tapestry might have appeared soon after it was woven (you need to take a bit of care with colour management too).

      A friend of mine did this as part of his PhD thesis. I can't find any of his images online (I guess there would be copyright problems), I'll see if I can dig some low-res ones up.

    • Gee ... may I ask, are you familiar with the expression "to know the price of everything, and the value of nothing"?

  • by aldeng ( 804728 )
    That's a lot of pie! Thanks, I'll be here all week.
  • by datbox ( 800756 ) on Monday April 04, 2005 @10:48AM (#12133744)
    One is a 1992 article about how they calculated pi to over two billion decimal places

    Hrmm.. They should've just rounded down? ;)
  • Pi Accuracy (Score:2, Interesting)

    How do you ascertain that your 2 billion decimal places of pi are correct? After about 50 significant decimal places doesn't the accuracy get too small to test against reality? There are formulas for calculating pi but it would then seem that your "accuracy" in calculating pi just depends on which formula you chose and how big your power bill was that month. Is the act of calculating pi still a modern yardstick of computer accuracy or is this just what you need to do to get a feature in the New Yorker?
    • Many infinite series have error bounds to prevent just this sort of thing.
    • Re:Pi Accuracy (Score:5, Insightful)

      by mikeplokta ( 223052 ) on Monday April 04, 2005 @11:43AM (#12134226)
      Pi's definition is mathematical, not physical. No one really knows the exact ratio between the circumference of a circle and its diameter, but it definitely varies depending on how curved space-time is in the vicinity of the circle, and on the size of the circle.

      Pi is 4 x (1 - 1/3 + 1/5 - 1/7 + 1/9 + 1/11 ...). (Or the limit of that series as its length tends to infinity, for the mathematical formalists among you.) Your accuracy in computing pi depends on how many terms of the series you can calculate (actually, there are alternative formulations that converge much more rapidly, but are less easy to write down in ASCII.)
  • by Cranston Snord ( 314056 ) on Monday April 04, 2005 @11:01AM (#12133856) Homepage
    David informed her that the brothers would need to obtain the complete set of raw data from the Leica camera. The next day, he went to the museum and collected, from Bridgers, two large blue Metropolitan Museum shopping bags stuffed with more than two hundred CDs, containing every number that the Leica had collected from the Unicorn tapestries. There were at least a hundred billion numbers in the shopping bags.

    Bags...and...bags...of numbers!
    • If they'd used 4.7GB plain ol' single-layer DVDs, it would have been 200/6.714... = just under 30 full DVDs. Which would have fit on a single spool. My "Babylon 5" collection takes up more space. And they chose to, what, put two hundred CDs in jewel cases to take them across the street? What a buncha maroons.

      --grendel drago
  • by whitehatlurker ( 867714 ) on Monday April 04, 2005 @11:04AM (#12133880) Journal
    ... when the paper has to illustrate what a circle looks like when explaining 'pi'.

    "Here is a circle, with its diameter:"

    • Frink: [drawing on a blackboard] Here is an ordinary square....
      Wiggum: Whoa, whoa - slow down, egghead!
      Frink: ... but suppose we extend the square beyond the two dimensions of our universe, along the hypothetical z-axis, there.
      Everyone: [gasps]
      Frink: This forms a three-dimensional object known as a "cube," or a "Frinkahedron" in honor of its discoverer, n'hey, n'hey.
  • several months?? (Score:2, Interesting)

    by Anonymous Coward
    These guys are pretty inefficient or they wrote a bunch of software from scratch.

    This is basically a classic close range photogrammetry problem. In fact even easier than that, a tapestry is essentially a "flat" scene (think throwing a bunch of kitchen utensils in a pile on the floor and constructing a scene out of it which is more typical of this type of problem. Or photographing the inside of a chemical plant and reconstructing accurate blueprints).

    At work we can process 50GB worth of aerial mosaics pe
    • by leoval ( 827218 ) on Monday April 04, 2005 @11:23AM (#12134048)

      I disagree with your analogy. Aerial mosaics have nothing to do with the work that the brothers had to accomplish.

      For instance, in aerial photagraphy the landscape being photagraphed changes very little if it changes at all (most of the changes are not even perceptible at the resolution of the cameras). Therefore reconstructing the full image is pretty much trivial (finding the overlapping sections is straightforward).

      In this case, and from TA, the images changed from frame to frame! because of several factors, temperature, humidity, light conditions etc. Also the paper cover that the photographers used also disturbed the fine threading in the images. So determining the overlapping sections between tiles could not be easyly automated, in fact from the article it seems that they were not even discernible with the naked eye.

      I thing that the time spent in that project was actually productive, and that in the process a bunch of original algorithms were created (I hope they are published in some place).

    • In the article, they say that they solved the equations by hand, and programmed it from scratch. They were given photographs of a "flat" scene at such a close range that it caused perspective issues with the height of the threads in the tapestry...

      a tapestry that was suspended in purified water, free floating in 3 dimensions...

      with a camera that was held at varying heights above the tapestry, since they were suspended by scaffolding over the work of art...

      art that was bumped by the photographers as they
  • Pi (Score:2, Interesting)

    The unefulness of calculating pi to this number of digits is nill. After about thirty digits, you have the orbit of the earth calculated, with an accuracy equal to the size of an atom. Computing the circumference of a circle with diameter equal to size of known universe takes about fifty digits.

    The only interesting part of all this is the way that the algorithms (invented by Al Gore, hence the name) to calculate have become lossless in binary.

    Part of the issue I had when I was in grade school and crate my
    • Re:Pi (Score:3, Informative)

      by leoval ( 827218 )
      I agree with you, I don't think that practical uses for the billionth digit of pi will be found in the near term. However exploring Pi is a good exercise for numbers theorists because it allows them to peer inside the irrational numbers and their properties. There is still a lot if uncharted territory in that area. One of the most sought after peculiaritis of an irrational number (Pi in particular) is to check if any kind of patterns can be discerned in the long list of decimal digits.

      Carl Sagan, dreamed l
      • Was this Carl Sagan, or Isaac Asimov?
        • Re:Pi (Score:3, Informative)

          by Hooptie ( 10094 )
          It is Sagan and it happens at the end of Contact (the book not the movie)


      • "Carl Sagan, dreamed long ago (through one of his characters) to find a "circle" pattern inside Pi (i.e another series of Pi inside)."

        We will.

        Assuming that pi is random (thought to be true), and that it never ends (known to be true), *any* fixed-length string of numbers can be found.

        So, yes, a circle can be found in the digits of pi. As can my phone number.

        Now, the longer the string you want to find, the further you have to go.
        • Assuming that pi is random (thought to be true), and that it never ends (known to be true), *any* fixed-length string of numbers can be found.

          This is a nit-pick, but I think it needs to be said:
          Pi is NOT random. Random and irrational are two entirely different things.

          A serious question though: Is it true that any fixed length string of numbers can be found in pi? If pi were random, the answer is "yes", however, I do not believe that this MUST hold true for an irrational number. If anyone knows if this ha
    • Re:Pi (Score:3, Interesting)

      by Ironsides ( 739422 )
      The only interesting part of all this is the way that the algorithms (invented by Al Gore, hence the name)

      Not sure if this is meant to be a joke or not but...

      Algorithm, as it is used in mathematics means a systematic procedure to solve a problem. The word is derived from the name of the Persian mathematician, al-Khowarazmi (See algebra). The first use of the word I am aware of was by G W Liebniz in the late 1600.

      Source: []
      Other Source: []
    • Earth's orbit is a circle? News to me! Accurate to within the size of an atom? Yeah because the center of mass of the earth never changes, right?

      Funny thing is, I have mod points, but rahter than modding this down, I wanted to point out how inaccurate it is, lest someone else just mod it up again.

      I particularly like the line about calculating the circumference of the known universe. The number of digits depends on the precision you need, not the size of circle. If you are having trouble understanding
      • Ummmm. You missed the point entirely. Yes, the orbit of the earth is not a circle. And computing the circumference to have an error the size of an atom was implied. And yes, that precision is dependent on the diameter of the circle. Go back to grade school math.
        • It's not a circumference. There's no circle. You're rambling. Goign back to school has nothing to do with it, you are either a complete moron or a very clever troll.

          Judging by your searching my archives and bringing up my roland P post, I'm going to guess it's the latter.
          • I take back the part about going back to school.

            However, I think you are deliberately misunderstanding my prior post. Would it have been better to say: "Given a circle with a radius equal to 1 AU, you could measure the circumference to the size of an atom by using a value of pi with 30 digits or so"? Yes, it would have been more accurate. But I wrote it the way I did for ease of reading. Everyone else understood what I meant.

            The point is that length of pi calculation in and of itself is meaningless. Beyon
            • Planck's constant is a unit of energy, it wouldn't be measured in meters.

              And, as many others here have pointed out, the digits of pi aren't calculated for some direct beneift. They are calculated to study the properties of irrational numbers, as well as to provide a test bed for computer hardware and algorithms.
              • The plank unit is NOT a unit of energy. Go look it up

                And I made your second point in the original message.

                You are a troll.
                • Crap - I looked it up. The unit can refer o either energy or length. Nevertheless, the original message is correct, and I stand by the fact you are a troll.
      • Kinda funny that someone who complains about Roland P's posts would himself be using Slashdot for his own game.

        And man do you have a potty mouth.
    • The real problem with using 4*(1 - 1/3 + 1/5 - 1/7...) to approximate Pi, as any Calc II student knows, is not exactly rounding error but rather that it takes a freakin' long time to converge! The error when using n terms in this series is approximately 1/(2*n+1), which means to get 14 digits correct you need 5*10^13 terms. Rounding error comes into play only because you start to accumulate significant error when doing that many additions; almost every floating-point computation has rounding error though.
  • Wachowski brothers - The Matrix and other films

    Chudnovsky brothers - Supercomputers

    I have no brother. Now I know why I'm an utter failure. Oh well, back to Slashdot.

  • Somebody enlighten me. Is there any use in knowing Pi to 2 billion decimal places (or even just a few hundred!) Do we hope to find a hidden message, or make the world's most accurate circle, or is it just because we can calculate it? And how do you check for errors?

    • Some people believe it holds insight into patterns. Thus if you could crack PI, you could crack the stockmarket, the bible, etc.

      See the movie:
      PI []

      There are also several interesting books on the topic including The History of PI, by Peter Beckmann.

      The Life of Pi by Yann Martel, however, has nothing to do with the number.
    • Somebody enlighten me. Is there any use in knowing Pi to 2 billion decimal places (or even just a few hundred!) Do we hope to find a hidden message, or make the world's most accurate circle, or is it just because we can calculate it? And how do you check for errors?

      Well, on the question of hoping to find a hidden message, TFA says:

      They wonder whether the digits contain a hidden rule, an as yet unseen architecture, close to the mind of God.

      Aside: this reminded me a lot of the movie Pi []. I have to won

  • Film (Score:5, Interesting)

    by kinzillah ( 662884 ) <> on Monday April 04, 2005 @11:21AM (#12134037)
    rather than stich a bunch of digital photos, they should have simply photographed it with a very large format camera, and had the resulting negative drum scanned at 8000dpi. These folks [] do it that way, and if you take a look, the resolution is amazing.
    • Re:Film (Score:2, Insightful)

      by myukew ( 823565 )
      maybe they had no 8000dpi scanners back in a time when normal people could build one of the fastest supercomputers in the world and pay less than $80k
      • WTF? Insightful? How?
        These are 2 separate projects, one recent and one old. They have nothing to do with each other. It thus doesn't matter whether there were 8000dpi scanners when they built the supercomputer.

        Poster and moderators on crack with this one ;)
    • ...or dont do it at all!!!

      Your r on /. baby... remember that ;)

    • Re:Film (Score:2, Informative)

      by BalloonMan ( 64687 )

      rather than stich a bunch of digital photos, they should have simply photographed it with a very large format camera, and had the resulting negative drum scanned at 8000dpi.

      Works great for landscapes at infinite focus, but not so great for up-close work. To avoid nasty spherical aberations, they would have to shoot the tapestry through a mega-telephoto lens from 100 yards away, but the walls of the museum would kinda get in the way. And it can't be just any large format camera, either. Scanning at 8000 d

    • This is much higher resolution than the gigapixel people. And digital has better colour than film (though it's not clear how much colour management the Met's photographers did).
    • Screw the negative; why not scan the tapestry itself at 8000dpi? Just wrap it around the drum, and voila!

      I'd hate to see it jam, though... ;-)

  • I understand the reason for fixing it to have a record of what dot went where for restoration into the future, but I wonder if they isolated out each thread's color so that people can experiment by replacing the "red" threads with a given new "red" and stuff like that without having to mess with the original. You more or less have to use the real thing if their image doesn't allow this, which would be a total waste in terms of usefulness to art historians.
  • by Anonymous Coward
    Everybody seems to think the middle ages were some kind of throw-back. Because Roman civilization was gone, people think that Europe had sunk back nearly to the stone age. In particular, they think that because the art is not photo-realistic that it must be primitive.

    This tapestry embodies a culture that we no longer understand. In fact, the makers of the tapestry may not have completely understood the references they were making. (Just as we don't. Think of all the figures of speech that you use and
  • Billion Places Of Pi (Score:3, Interesting)

    by Pants75 ( 708191 ) on Monday April 04, 2005 @11:48AM (#12134276)
    Quick question...

    How do we *know* that pi is exactly the result of the formulas that these people use to calculate pi?

    I only ask because I assume that pi (as defined by the number of times the diameter of a circle can be wrapped around its circumference) might differ at some arbitary point into the calculation?

    How do we know that these calulations actually produce a number that matches reality?


    • You're making the incorrect assumption that Pi is *defined* in terms of the ratio of a circle's diameter to it's circumference.

      Your definition is incorrect. Pi is **defined** in terms of the mathematical power series that many others have posted.

      It just so happens that this is ** APPROXIMATELY ** The ratio of a circle's circumference to it's diameter, in FLAT EUCLIDIAN SPACE. If space is curved, then the ratio does NOT correspond to Pi. (e.g thing of a circle drawn on a partially inflated ballon, then in
    • In fact, it doesn't. This is a result of the fact that space time is curved, which causes the ratio between diameter and circumference to change.

      That said, in a perfectly flat euclidian space, all of these formulae are proven to result in pi, or else they wouldn't use them. The proofs, however, may be a bit on the complex side.
  • by Anonymous Coward on Monday April 04, 2005 @11:50AM (#12134293)
    Meh.. you guys are missing the forest for the trees.

    Who cares whether they calculated Pi to n-billion digits? Who cares if they photographed the tapestries to the precision of an atom??

    The important question that needs to be answered is: how did they end up with wives who (a) work; (b) don't force these two nerds to work; and (c) let them buy all the toys they need? Where can I get a wife like this??

  • You call Google the world brain? I hear they are renaming it skynet.
  • by Jugalator ( 259273 ) on Monday April 04, 2005 @12:12PM (#12134523) Journal
    Has any numerical analysis been done to its decimals to find any particularly mathematically or esthetically "interesting" sequences? Anyone know any links to websites for that? The "monkeys banging on a typewriter" thing. :-)

    I mean, with an enormous amount of decimals calculated, you'd think there was some pretty cool sequences in there?
  • The first problem: They hired amateurs to photograph priceless artifacts. Though the description is short it does include some tip-offs, "skateboard wheels." Sounds like they hired some real flakes that couldn't control the environment they were photographing and they were using inexpensive equipment... I applaud the brothers for their work but it seems like a wasted effort because it could have been avoided if they had hired professionals to photograph the damn thing.
  • Why is it that despite the Chudnovsky Brothers claims, which no one doubts, there doesn't seem to be any pictures of their apartment supercomputer? Does it still exist? Is it still running? Is it still computing PI? One would think that a machine that allowed them to compute so many digits of PI would be "immortalized" with at least one image, right? Can anyone point me to pictures?
    • by cr0sh ( 43134 )
      I read both New Yorker articles, and still, no pictures, nothing - googling and GIS searches seem to help not one bit. It isn't that I doubt the claims, I have no reason to doubt them. However, one would think there would be more than just a few pictures. It is madenning.

      I have watched the movie PI - and I know that in part it was based on these two. I think about the computer as depicted in that movie. I think about other people I have known and about myself. I have known people who have had "vast collecti

      • I think the point is 1) they have a very immersive cerebral life and 2) they are building the NSA's next supercomputer and mum's the word. But 3) they are probably wonderfully friendly and might even be willing to invite you over if you have something interesting to say to them.
  • 70 billion? (Score:3, Funny)

    by PenguinX ( 18932 ) on Monday April 04, 2005 @01:54PM (#12135593) Homepage
    That seems excessively irrational.
  • With this kind of processing power, a project of mine which I've always wanted to bring to birth, Infinity Generators, might be a reality.

    Take, if you will, a simple 640x480 image, with 256 colours. (It could be any image size and any number of colours, but this is just a standard image format). With it's 640x480 dimensions, there are a total of 307,200 pixels. If each pixel can have one of 256 colours, thats a total of 307,200^256 = 6e+1404 possible permutations of that image.

    Such a system as this co
  • There sure was too much breathless fawning in that article. These men are extremely sharp. Let there be no doubt. While I cannot rule it impossible, I have never heard of someone who needs such air filters. I have heard of hypochondriacs. It's praise praise praise. It might be perfect for a New Yorker reader who does not know much, but wants to feel edified.

"Call immediately. Time is running out. We both need to do something monstrous before we die." -- Message from Ralph Steadman to Hunter Thompson