## 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."*
## Gigabyte, gigapixel artwork? (Score:5, Funny)

:)

## Re:Gigabyte, gigapixel artwork? (Score:5, Interesting)

## Re:Gigabyte, gigapixel artwork? (Score:2)

You mean like mapquest.com or maps.google.com?

## Re:Gigabyte, gigapixel artwork? (Score:4, Informative)

## Re:Gigabyte, gigapixel artwork? (Score:2)

## Re:Gigabyte, gigapixel artwork? (Score:2)

## Re:Gigabyte, gigapixel artwork? (Score:2)

Here [nasa.gov] is an 8192x4096 of Earth. Created as a mosiac with 1km square tiles with no clouds

A version [nasa.gov] with clouds is also available.

Here [nasa.gov] is a 30000x15000 (yah, you heard me) GIF of the entire planet's city lights at night.

A 16394x8192 [nasa.gov]

## Re:Gigabyte, gigapixel artwork? (Score:2, Informative)

## If you're in New York (Score:5, Informative)

## Re:If you're in New York (Score:2, Informative)

## Northern tip... (Score:4, Funny)

mile(and change) of Manhattan north of the cloisters.Either that, or my apartment is actually in Yonkers and I should be paying a lot less rent.

## Re:I don't wanna sound like a queer or nothing (Score:2)

Obligatory PBF link:

http://cheston.com/pbf/PBF024ADUnicorn.jpg [cheston.com]

## Link (Score:2)

Prepare for a cataclysmic event.

## Re:Link (Score:2)

## April fools (Score:5, Funny)

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.

## The Cloisters at the Met (Score:5, Informative)

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).

## Re:The Cloisters at the Met (Score:2)

## Re:The Cloisters at the Met (Score:2, Funny)

## The hardest technical problem... (Score:5, Funny)

## Re:The hardest technical problem... (Score:4, Funny)

## Re:The hardest technical problem... (Score:2)

## Why? (Score:2)

## Re:Why? (Score:5, Informative)

## Re:Why? (Score:2)

## Re:Why? (Score:2)

## Re:Why? (Score:5, Interesting)

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.

## Re:Why? (Score:5, Interesting)

## Re:Why? (Score:2)

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

## Gigapixel pie? (Score:2, Funny)

## What were they thinking?? (Score:4, Funny)

One is a 1992 article about how they calculated pi to over two billion decimal placesHrmm.. They should've just rounded down?

## Pi Accuracy (Score:2, Interesting)

## Re:Pi Accuracy (Score:2)

## Re:Pi Accuracy (Score:5, Insightful)

Pi is 4 x (1 - 1/3 + 1/5 - 1/7 + 1/9 + 1/11

## Re:Pi Accuracy (Score:3, Informative)

## Re:Pi Accuracy (Score:3, Informative)

## Re:Pi Accuracy (Score:3, Informative)

## Re:Pi Accuracy (Score:2)

## Re:Pi Accuracy (Score:3, Informative)

## Re:Pi Accuracy (Score:2)

## New Unit of Measurement (Score:5, Funny)

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!

## Uh, DVDs anyone? (Score:2)

--grendel drago

## Re:Uh, DVDs anyone? (Score:2)

and completedin 1998?Anyway, the whole thing'd fit on a Blu-Ray now. Not impressive at all. I mean, Metallica's latest requires a huge pile of CDs for the WAVs, but that ain't too impressive...

## Gotta wonder about "The New Yorker" readers ... (Score:4, Funny)

"Here is a circle, with its diameter:"## Obligatory... (Score:3, Funny)

Frink: [drawing on a blackboard] Here is an ordinary square....Wiggum: Whoa, whoa - slow down, egghead!Frink: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)

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

## Re:several months?? (Score:5, Insightful)

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).

## Depends on your definition of flat (Score:2)

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 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)

Carl Sagan, dreamed l

## Re:Pi (Score:2)

## Re:Pi (Score:3, Informative)

Hooptie

## Re:Pi (Score:2)

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.

## Re:Pi (Score:2)

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)

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: http://www.pballew.net/arithme1.html [pballew.net]

Other Source: http://www.disc-conference.org/ [disc-conference.org]

## Re:Pi (Score:2)

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

## Re:Pi (Score:2)

## Re:Pi (Score:2)

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

## Re:Pi (Score:2)

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

## Re:Pi (Score:2)

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.

## Re:Pi (Score:2)

And I made your second point in the

originalmessage.You are a troll.

## Re:Pi (Score:2)

## Re:Pi (Score:2)

And man do you have a potty mouth.

## 4*(1 - 1/3 + 1/5 - 1/7...) is a bad choice (Score:2)

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.## Re:4*(1 - 1/3 + 1/5 - 1/7...) is a bad choice (Score:2)

## [A-Z][a-z]*sk[iy] brothers (Score:2, Offtopic)

The Matrixand other filmsChudnovsky brothers - Supercomputers

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

## Re:[A-Z][a-z]*sk[iy] brothers (Score:2, Funny)

## Re:[A-Z][a-z]*sk[iy] brothers (Score:2)

## Why do you need to know Pi so accurately? (Score:2)

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?

## Re:Why do you need to know Pi so accurately? (Score:2, Informative)

See the movie:

PI [imdb.com]

There are also several interesting books on the topic including The

History of PI, by Peter Beckmann.The Life of Piby Yann Martel, however, has nothing to do with the number.## Re:Why do you need to know Pi so accurately? (Score:2)

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

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

## Film (Score:5, Interesting)

## Re:Film (Score:2, Insightful)

## Re:Film (Score:2)

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

## Re:Film (Score:2)

Yes, that is what the parent of your original post said. And then you said that maybe that didn't exist back when you could make a supercomputer for $70000.

Really man, lay off the crack.

## Re:Film (Score:2)

## Do it the Geek way... (Score:2)

Your r on

## Re:Film (Score:2, Informative)

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

## Re:Film (Score:2)

## Re:Film (Score:2)

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

## they "fixed" it, but did they get the threads? (Score:2)

## The middle ages weren't that simple (Score:2, Interesting)

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)

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?

Pete

## Re:Billion Places Of Pi (Score:2)

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

## Re:Billion Places Of Pi (Score:2)

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.

## Re:Billion Places Of Pi (Score:5, Informative)

pi^2 / 6 = Sum_{n=1}^{oo} 1/(n^2)

It is straightforward to prove this identity. (Just take Fourier coefficients on the function f(x) = x on the interval -pi to pi).

If you're looking for an experiment with 2 billion significant digits of accuracy, you're never going to find one. That's physically impossible, for several hundred reasons.

## Re:Billion Places Of Pi (Score:2)

## Missed the real story... (Score:4, Funny)

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??## Re:Missed the real story... (Score:2)

(for those who didn't RTFA, or who jsut plain missed it, the Chudnovsky brothers are from there.)

## The world brain? (Score:2)

## With pi calculated with so many decimals... (Score:3, Interesting)

I mean, with an enormous amount of decimals calculated, you'd think there was some pretty cool sequences in there?

## Re:With pi calculated with so many decimals... (Score:2)

Look me up some time

## wow... waste of processor cycles! (Score:2, Insightful)

## A question... (Score:2)

## Upon further reading... (Score:3, Interesting)

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

## Re:Upon further reading... (Score:2)

## 70 billion? (Score:3, Funny)

## Generating Infinity.... (Score:2, Funny)

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

## Breathless junk (Score:2)

New Yorkerreader who does not know much, but wants to feel edified.## Re:Looks fine to me... (Score:2, Insightful)

Why do we need anything more than the low-res picture that they already have? Going super-high-res simply magnifies the imperfections. Art isn't meant to be enjoyed with your face pressed up against it.This has got to be one of the most short sighted posting on

## For a photo? (was Re:Looks fine to me...) (Score:2)

Does anyone remember what the comparable dpi for, say, 35mm photos? Say

I want to blow it up to the size of the original tapestry?