Gigapixel Tapestries & Gigadecimal Pi

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."

Comments

If you're in New York

[seringen]

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!

The Cloisters at the Met

[Speare]

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).

Re:Why?

[Speare]

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.

Re:Pi

[leoval]

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

Who knows, perhaps something interesting will be found.

Re:Gigabyte, gigapixel artwork?

[Speare]

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.

Re:Billion Places Of Pi

[poopdeville]

Uh, pi is the limit of a convergent sequence. One can easily derive identities with which to calculate pi to any accuracy desired. A simple one is:

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.