Michael Barnsley: The Poetry of Data Compression
Pictures, be they on TV, paper or the Web, are the currency of American communication and imagination. How pictures are made and manipulated affect our view of the world. Now, math is going change the way images are created and used, from the pictures on your television and computer screen to billboards and magazines. How? Fractals . . . .
Atlanta entrepreneur Michael Barnsley believes that fractals could revolutionize the world of digital imaging. Barnsley's field is fractal geometry, the branch of mathematics that describes irregular, recurring shapes in nature such as ferns, clouds, rock formations -- shapes with repeating patterns. Fractal geometry can describe a collection of potato chips as precisely as Euclidean geometry can describe a collection of rectangles. A few fractal equations can reproduce a scene while using only a fraction of the data required for pixel-based computer images. The same image could be used for pictures in any medium, without loss of quality, and could be sent over the Web using only a tiny portion of the data and time now required. And the same image could be used for a postage stamp or a billboard.
Digital imaging is exploding and the technology is not keeping up with the convergence of industries: digital cameras; digital television; the Internet; print media; interactive media (e.g. video games, interactive kiosks, etc.). These digital image markets share similar challenges: Effective bandwidth for images is actually decreasing, higher speed modems in every home is still a dream, image quality must be maintained at lower cost and time investment.
Barnsley is, of course, not the only technological visionary who sees the "Big Picture." What makes Barnsley special is that he sees the little ones as well -- and has figured out how to transform big ones into little ones and back again. That, as it turns out, is a handy and well-paying trick to know when it comes to the problem of compressing pictures or any other data for transmission over computer networks.
"Data compression, how boring!" you might say -- but you'd be wrong. Try to picture Barnsley, a Yorkshire-born Englishman, leaping with excitement to the blackboard of his very modern but very cluttered office, as he explains the universe to you. There, with arms flying as he searches in vain for a "duster" to clean away a jumble of equations left from some other conversation, he explains that data compression is another form of poetry. "Yes, poetry! That's exactly the nature of poetry -- a compression of thoughts and feeling into highly concentrated form. In fact, compression is at the heart of ALL communication. Think about the alphabet. In English, we take just 26 characters and by some miracle we capture, with amazing efficiency, an entire rich and infinite language!"
Having finally found the eraser, Barnsley now has cleared enough of the blackboard to allow him a small amount of working space. The knowledge that it's there to receive new equations seems to calm his nerves. With an undergraduate degree from Oxford University and a Ph.D. from the University of Wisconsin, the 52-year-old Barnsley is a world-class mathematician who's been mentioned as a candidate for a Nobel Prize. He is the very model of an English math professor -- charming, a bit eccentric and quite brilliant.
He's the son of the English novelist and painter Gabriel Fielding, who took his pseudonym from a famous forebear, the great 18th century novelist Henry Fielding, author of Tom Jones. His voice has no real trace of an American -- let alone Southern -- accent, though he's lived in Atlanta since 1983 when he came to teach mathematics at Georgia Tech. Nor, in his loose cotton shirt and corduroy trousers, does he project the image of the astute businessman who in 1987 co-founded (with fellow mathematics professor Alan Sloan) the high-tech company called Iterated Systems, so named because it describes the repetitive nature of fractalsystems.
It's clear that Barnsley loves explaining mathematics, and in fact he's just finished writing, narrating, and starring in a new film for Public Television called "God's Thumbprint." In addition to dozens of abstruse technical works, he has written the popular book, Fractals Everywhere.
At the board, he draws a line (call it "C") and then divides the segment C into two parts and labels them A and B.
"Now we see something quite amazing," he says, in a kind of awe. "Simple, and yet astonishing! Look! Notice that A and B are just little copies of C. Do you see? That's all they are, little COPIES. Well, BINGO! -- what that means is that space is the same in all sizes, so you can magnify spaces or you can shrink them. The flat abstract plane imagined by the ancient Greeks has this marvelous property of stretchability -- you can shrink it or expand it without limit. Well, so WHAT? Good question! Here's what: you can take any line segment, or triangle, or any other shape at all, and transform it into a bigger or smaller version of itself. Think about a yardstick. Each one-inch segment is a copy of the whole yardstick, and at the same time the yardstick is a copy of each one-inch segment. This is BIG NEWS!"
Furiously, he scrawls a picture of a yardstick, and then some little segments on that yardstick, and then some right triangles of many different sizes in many different positions.
"Do you see? Look at these shapes. By a simple formula -- a formula I call a 'transformer' (a mathematical transformer, not an electrical one) -- you can make a tiny copy of a very big shape, and then from that tiny copy you can recreate the big shape whenever and wherever you want to! You can think of the transformer as Michael's magical photocopy machine, which has two lenses, one to enlarge and one to shrink, and you can shrink and enlarge shapes over and over and over again, in an iterated process. It's as good as magic!"
In order to return to the chair behind his desk, he has to squeeze between file cabinets and stacks of boxes and several computers. At one and the same time he is both oblivious to, and absolutely amazed by, the physical world he captures in equations. He doesn't see his crowded office full of boxes as a clutter, he sees it as a challenge -- and when he explains data compression he talks of it in terms of fitting boxes into the trunk of a car.
His visitor asks diffidently, "Well, I can see how you can shrink and stretch line segments and triangles, but how do you compress or enlarge a jumble of objects with no apparent order? How would you compress a photo of, say, this office -- a blackboard, two people talking, boxes, computers, file cabinets, a window, and so forth?"
"Good, good. Lovely question! The answer is that every bit of a picture can be explained in terms of the picture itself." He flies back to the board, and dashes off a picture with different sorts of objects -- people, boxes, computers, etc. "A picture is just a collection of edges, smooth surfaces and textures. And so you can explain a big picture in terms of little pictures, and you can create big pictures by a process of iteration -- repeating little pictures of edges, surfaces and textures over and over again to transform all the little pictures into a big picture. A tiny patch of a blue wall is a small picture of the wall itself, and can generate the bigger picture of the whole wall. How does fractal geometry come in? These transformations of irregular shapes are simply numbers -- numbers which describe a shape and its relation to other shapes. It's a miracle formula. You don't keep the shapes themselves, you keep the fractal transformer that describes the shapes and their relationships with other shapes. What you do is you roll out Michael's magical photocopy machine, and recreate the picture where those relationships were found. It's great fun!"
Besides being fun, it's also profitable. Iterated Systems has developed products for a wide range of image-intensive industries: prepress, graphic arts, media asset management, digital photography and digital video. Industry giants like Microsoft, Nike, Miller Brewing and Wieden & Kennedy, the nation's leading ad agency, are using fractal technology from Michael Barnsley's Iterated Systems, Inc., to produce high quality ads and images faster, cheaper and better. RealNetworks, Microsoft, Mitsubishi and Oracle, among others, use the technology. CD-ROMs that use Iterated's technology include, Encarta Microsoft, Encyclopedia Grolier, Great Artist Attica, 20th Century Video Almanac Mindscape. Screen savers include Golf Digest-Parsons Technology, Sharks-Expert Software, Twilight Zone-Sound Source and Star Trek Screen Posters-Berkeley Systems.
Barnsley's next mission is to convince the computer industry to use highly compressed fractals to replace big inefficient gobs of pixels, in order to vastly improve both picture quality and transmission speeds.
Barnsley's mission could change the nature of the Internet. Get the picture? It's a Big one.
And Dr. Barnsley is again on the move. He recently left Iterated to found yet another software company, SpringSoft, focused on the application of fractal theory. In addition, he accepted a professorship at the University of Melbourne, and so he and his family will spend part of each year in Australia and he will run the business operation from both sides of the Pacific.
Arnold Davis writes frequently on technology and education.