# Beyond Dotty Images: How Computers Paint

Beauty may be in the eye of the beholder. But what if that beholder is silicon, copper wires, and lasers?

And that breathtaking outline of a billowy cloud backlighted by the sun may be hard to put into words. But try describing it in a digital language so a computer or digital camera can re-create the finger-like tresses and almost infinite shades of color and light.

While the naked eye can take in these fine details of life, a digital device like a computer typically converts an image into a grouping of dots or pixels. It is difficult to make a crisp picture that way.

A series of dots comprising the edge of the cloud creates a uniform, scalloped image rather than the wisps we see in nature. Making the dots smaller refines the image, but it still leaves out the minute details of the irregular edges.

A new graphics technology is emerging that claims to re-create images more accurately and in more detail. It promises better images on the Internet, personal computers, digital cameras and future consumer devices.

The technology uses fractal geometry, simple mathematical formulas that describe odd shapes and edges quite precisely so that a digital device can reproduce them true to form. Fractal geometry can describe the shape of a cloud as precisely as an architect can describe a home. And fractals can be reduced or magnified, intact, an infinite number of times.

"Fractal geometry opens up the class of shapes and forms we can describe succinctly by formulas," says Michael Barnsley, a mathematician and co-founder of Iterated Systems Inc., an Atlanta-based company that makes software that creates pictures out of fractal equations.

"With pictures you always run into a resolution problem because they are described as an array of dots," he adds. "That's why a digital camera necessarily takes a low-resolution, dotty picture."

A fractal is an extremely irregular curve or shape, any part of which is similar in shape to a larger or smaller part when magnified or reduced to the same size. Take a fern. Its forking branches recreate themselves on an ever tinier scale as you look from the entire plant to each leaf blade, and then to its leaflets and their sub leaflets. There are almost limitless examples of fractals in nature.

One benefit of fractal geometry is that it minimizes or compresses data about the image, so less space is needed for a digital device to store images. This means high-resolution pictures can be sent across the Internet more quickly and cheaply, and more can be stored in a computer's hard-disk drive and later printed onto paper.

Rather than store a set of data that describes every pixel, a fractal image file contains a record of repeated patterns that exist in the image. Each fractal equation can be iterated many times by reusing one equation as input into the next to replicate self-similar details into a full picture.

The first fractals - a line and a right-sided triangle - were known by Plato and Ptolemy more than 2,000 years ago, but it wasn't until the mid-1970s that an IBM Corp. mathematician actually coined the term "fractal."

Benoit Mandelbrot of IBM's Thomas J. Watson Research Center discovered the most complex fractal known to exist, and recognized the existence of fractal geometry in nature. His work led others to think in a new scientific way about the edges of clouds and the profiles of the tops of forests.

Dr. Barnsley took the notion of fractal geometry one step further by creating a software program that takes the pixel images generated by computers and transforms them into fractal equations, and then once again into pictures. The subsequent pictures have more detail, because the fractal equations use artificial intelligence to fill in the details left out by the pixel.

Initially, the intense details and colors of fractal geometry computer images were more for entertainment than practical use.

The first big commercial use came in CD-ROMs for personal computers. Microsoft Corp.'s Encarta encyclopedia CD-ROM, which comes with many new personal computers, is one of the best-known examples using Iterated's fractal transform program. Another is the "Sharks" screen saver made by Expert Software Inc.

The technology then moved into the digital pre-press industry for magazine articles, brochures, ads, and billboards. Altamira Group Inc. of Burbank, Calif., is using Iterated's system to create pre-press graphics for the publishing, advertising, and other print industries.

The technology will enable World Cup sponsor Nike to use one fractal image to put a picture of the winning goal on the Internet or the side of a bus. In the future, Barnsley expects it to be used in digital cameras and possibly digital televisions.

Today's digital cameras produce poor images and they are expensive, partly because all the electronic circuitry is inside them. If a digital camera instead was made as a low-priced peripheral device that could be hooked to a personal computer to process and store its images, it would be affordable to many more people and the pictures would be better, Barnsley says.

Fractal technology still is in its infancy in the commercial world, but Barnsley and others have high hopes for it.

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