"Ikebana," one of Tim Fadden’s works, looks like a vase of flowers, but each tiny bubble among the swirling lines contains an image of the entire fractal — only much smaller and slightly different.

By BILL VARBLE

You won’t find Tim Fadden working out details of his images with pencil and paper like some artists. His fractals take 250 trillion computations to produce.

"Fractals turn math into art," he says.

A ground-breaking exhibit of fractals by Fadden and three other artists is hanging at JEGA Gallery in Ashland’s old railroad district through June.

"You won’t see anything like this in New York City," gallery owner J. Ellen Austin says.

The fractals were printed on a new LightJet 5000, which prints from a digital file using three monochromatic lasers onto Fujichrome paper to produce archival-quality images.

Looking at fractals is a bit like peering into eternity. "Ikebana," one of Fadden’s works, looks rather like a vase of flowers, but each tiny bubble among the swirling lines contains an image of the entire fractal — but very much smaller and just slightly different.

If you blew up one of these smaller bubbles you’d have a nearly identical image of the whole fractal, including a new batch of bubbles. Blow up one of these and you’d have another, and so on down through trillions of points of millions of colors.

"The fractal universe contains an infinite number of universes," Fadden says. "Each is nearly identical to the last. The deeper you go the more the pattern differentiates."

This is theoretically true out to infinity, but there are still limits in computers and software.

"Give me a bigger computer and I’ll give you a deeper universe," Fadden says.

Fractals may be snapshots of an infinite universe, but they are also graphic representations of geometry. A fractal is a rough or fragmented shape that can be divided into parts, each of which is a slightly different copy of the whole. It’s what mathematicians describe as unpredictable behavior in a deterministic system.

Clouds, mountains, coastlines, bark and lightning can be fractals. Many mathematical structures — including things only a mathematician could love, like the Sierpinski triangle, the Koch snowflake and the Peano curve — are fractals.

Fadden put together this show as an overview of the state of the art. It includes fractals by D’Orchid of Talent (who combines fractals with other images), Linda Bucklin of New York City, and Paul De Celle of Detroit, Mich.

Some of the images bear a passing resemblance to mundane objects. De Celle’s "Helcia" looks like a baroque horn and some busted-up clockworks. A 30-by-40-inch fractal of Fadden’s called "Peace" took 375 trillion computations yet has the organic look of feathers, wood and shells.

Fadden, 43, is a former painter, sculptor and photographer who holds degrees in psychology, physics and computer science. He ran a group home for adults with developmental disabilities before starting Singular by Design, a digital media design company in Ashland.

He says he views the computer as an extension of his body, almost like any other tool. He began making computer art in the 1980s and started experimenting with fractals four years ago.

"It took me about three years to get it wired," he says.

Using programs called TieraZone and GrafZViZion, he starts with a graph and manipulates it, choosing mathematical variables likely to yield the forms and colors in which he’s interested.

It’s the quality of printing now available that makes these images possible. The printer at Robyn Color, the San Francisco firm that printed these images, costs $375,000 and is the size of a small house.

"I’ve been waiting for printing to catch up to fractals," Fadden says.

These framed fractals carry price tags from several hundred to $2,000.

His goal is for fractals to be accepted as an art form, and for people to see the strange beauty that comes out of the technology.

"They’re still just scratching the surface," he says. "I expect it’ll become more dazzling."