When Internet surfers watched Keiko Matsui's contemporary jazz concert Sunday night, they had fractals to thank for the live broadcast from the House of Blues to the World Wide Web.

Squeezing all of the data required for a realistic moving picture over a computer modem--especially in real time--is a massive technical challenge. The House of Blues Webcast was the first to employ data-compression techniques based on fractals--the psychedelic geometric shapes that are made by repeating a small number of equations over and over.

Fractals are emerging as a promising solution for a host of data-compression problems involving still pictures, audio and video. Although fractals are complex shapes that take a considerable amount of computing power to draw, they are easy to capture mathematically. Fractal researchers hit upon the idea of inverting that process to reduce a complex image into a few math equations.

Typically, a compression program examines the picture elements, or pixels, that make up a digital image. Because each pixel tends to look a lot like the pixels surrounding it, a compression program can make a file smaller by storing only partial descriptions of each pixel.

Depending on the complexity and size of the original picture, traditional compression techniques can squeeze a picture that takes up between 15 and 25 megabytes of computer storage into a file roughly 30% its original size.

Fractals can squeeze many files even smaller by eliminating more data, researchers say. A typical file can be compressed with fractals to between 13% and 20% of its original size, and some pictures have achieved compression ratios of 40 to 1.

For example, a picture of a house contains several straight lines and corners. Rather than record each one separately, a fractal-based compression program can store just one line and one corner, along with instructions on where they should be drawn. Sound, which can be represented by a wave, is compressed the same way.

Moreover, a line is just as straight and a corner just as sharp regardless of its size. That makes it easy to enlarge a picture that is recorded as fractal equations without adding to the size of the compressed file.

"Fractals allow you to eliminate some of the redundancy and thereby store information more compactly," said Yuval Fisher, a researcher at the Institute for Nonlinear Science at UC San Diego.

Smaller files take up less space on a computer and can be transmitted over computer networks faster. That is especially important for video applications, which require a series of pictures to be drawn at the rate of several per second.

Researchers at Iterated Systems Inc. of Atlanta--whose 80-member technical staff includes 30 people who hold doctorates--developed an algorithm that can take an inventory of every single pixel in an image (a high-resolution computer screen contains 70,756 pixels per square inch), then figure out how many of them look alike.

The program simplifies the entire picture into a single equation that essentially tells a computer to draw one shape and repeat it a certain number of times, then draw another shape and repeat that a certain number of times.

"If you have a picture with a big blue sky in the background, in fractal terms you only need one piece of the sky and an instruction that says, 'This area is all the same,' " said Jim Caveto, Iterated's director of marketing.

About 60,000 people have bought the company's Fractal Imager to compress their images for easy transfer over the Web since it was introduced last year, and more than 1 million Net surfers have downloaded Iterated's free Fractal Viewer software to see them. The company has also licensed its technology to a host of other developers.

Altamira Group of Burbank used it to develop Genuine Fractals, a new plug-in for Adobe Photoshop that allows users to compress high-resolution images for the commercial printing industry into super-small fractal files.

"Fractals are so complex and require such massive computing power that it is just now becoming possible to use them," said Dennis Aubrey, president of Altamira.

Progressive Networks, the Seattle-based creators of RealAudio, incorporated an Iterated Systems technology called ClearVideo Live into its RealVideo product to broadcast live events--like the Matsui jazz concert--on the Web.

ClearVideo makes videos look smoother with a bigger picture and sharper resolution, said Brett Goodwin, Progressive Networks' group product manager for applications. Users have to download, for free, a special fractal decoder to use the technology.

In McLean, Va., a company called Emc33 is developing a chip to be installed in televisions and VCRs that could download an entire movie via a cable line or satellite in seven minutes or less.

"Without fractals, we probably wouldn't be doing this," said Emc33 spokesman Jim Crawford. "It's an extremely important component for us."