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Computational Origami and David Huffman
geeber writes "Here is an article about David Huffman's work in the mathematics of computational origami at the New York Times (soul sucking registration required). According to the article, computational origami, "also known as technical folding, or origami sekkei, draws on fields that include computational geometry, number theory, coding theory and linear algebra." David Huffman is also the inventor of Huffman coding used in MP3s and was mentioned prieviously here."
Huffman coding was one of the first codings used to compress data LONG LONG time ago, in a galaxy far far away where MP3's were billions of years yet to come in the future.
It is real cool to see such pioneering people still involved in new things.
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Hmmm.
...is in Mark Nelson's "The Data Compression Book".
What's especially nice is that the book walks you thru the various steps - minimum redundancy coding, adaptive huffman coding, arithmetic coding... so the improvements are introduced gradually and logically. Good stuff.
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Check Amazon for the book mentioned in the article: Origami Design Secrets: Mathematical Methods There are some related titles that also look good.
There are also some nice pictures of Huffman's origami here. The pictures also show Huffman himself doing the folding.
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For what it is worth, as the article submitter, I wrote in the submission a simple "(reg. required)." Apparently CmdrTaco thought "(soul sucking registration required)" was far more informative, and edited it thusly. Which really annoys the crap out of me. Way to be professional.
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If this interests you, be sure to check out Erik Demaine's work at MIT, Issei Yoshino's Super Complex Origami, HOYJO Takashi, Biruta Kresling's Keikki Bamboo folds, Robert Lang's Design Secrets of Origami, Robert Hull's Origami^3 compilation. Not all computational origami looks mathematical but the methods for getting to and end are clearly designed from step one. Quite frankly I understand very little of the math, but I can appreciate the elegance of an efficient fold.
Directly from the article : Most computational origamists are driven by sheer curiosity and the aesthetic pleasure of these structures, but their work is also finding application in fields like astronomy and protein folding, and even automobile safety.
:-P
I'm tempted to flame you like hell but well, it's just that I've read TFA. My bad, sorry!
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I took a class taught by Professor Huffman at the University of California at Santa Cruz. He was an excellent teacher and really enjoyed teaching. The class, Introduction to Cybernetics, included Huffman coding and some basic neural network stuff, but never once did he call it Huffman Coding. One thing I remember from his class was we had to use a lot of logarithms and the results would have to be something like 5*log2(7) + log3(5). This ruled out using a calculator or a computer for the most part.
He also frequently gave credit to Claude Shannon on information coding.
Sadly (or fortunately) I avoided his other class, due to the fact that the failure rate was 60% for people taking the class for the second time. I think the first time takers failed at 90%.
-Aaron
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Huffman coding is a way of representing some stream of symbols using bits in the most optimal way possible.
Essentially, it breaks down to using your bits in such a way that the most common symbols are represented by the fewest number of bits. The result is a prefix-free code, meaning that no string of bits that represents a symbol is part of the beginning of any other symbol. You'll never get both "01" and "010" representing something in a Huffman Code.
A Huffman Code is optimal, meaning that it results in the shortest possible way to turn symbols into strings of bits with a one to one mapping between a symbol and the bits that represent it. As a result, it's used in a lot of compression methods.
There are better methods, like arithmetic coding. Huffman coding assumes an integral number of bits used for each symbol. Arithmetic coding results in a scheme where you end up with, essentially, fractions of bits being used. Naturally, this requires a lot more computation. Huffman coding is relatively cheap, computation-wise, and it's pretty easy to do. This is why it gets used so much.
The really big deal about Huffman Coding, however, is that you can *prove* that it's the most optimal method for doing what it does. That was Huffman's big accomplishment, really. Shannon-Fano coding is similar to (but not the same as) Huffman coding, but Huffman can be proven to be the optimal way of doing it.
There was also an article in Computer World Magazine, about Robert Lang's software that's being used to fold stuff from airbags to solar panels in spacecraft.
This folding project is not a Huffman or Lang, and it's not as impressive as those pictured in the Times article, with their sweeping curves and elegant surfaces. However, it does have a small element of the amazing "How do you get paper to DO that" quality. Best of all, it's fairly easy to fold and to improvise upon. Enjoy:
http://www.sgi.com/grafica/fold/page001.html