IMAGINE dropping by to watch Giotto paint frescoes in Italy's Scrovegni Chapel seven centuries ago. Or helping archaeologists excavate the ruins of the New York Public Library far into the future.
Artist Adrianne Wortzel grants such liberties to the characters in her intriguing work, ''The Electronic Chronicles.'' But you won't find this piece of art in a gallery or museum. It exists only on the World Wide Web, a region of the Internet that lets programmers display text and images in a format called a site or page.
Ms. Wortzel is not alone in trading her brushes and oils for a keyboard and mouse. According to a computerized search of the Web, the number of people who have posted their art in cyberspace runs into the thousands.
The first forays into this new frontier, however, are producing uneven results. For every site as elegant and witty as ''The Electronic Chronicles,'' hundreds more fall short in aesthetic and intellectual appeal. A significant number use language or images that some viewers might find objectionable, or at the very least inappropriate for children.
There are many redeeming sites, and the art world is taking them seriously. Web projects are expected to make a strong showing next year at such major exhibitions as ''Documenta X'' in Kassel, Germany, and the Whitney Museum of American Art's biennial in New York.
It remains to be seen how curators for these exhibitions will show work that so lacks physical presence. People go to museums to see the real thing, but on the Web there is no difference between an original and a copy. You can get the same experience at a library, cafe, or other place offering Web access. And yet curators do not want to miss what they perceive as a significant artistic development. Their problem, like many questions concerning the Internet, remains unresolved.
''For me, cyberspace is a new territory that's still white on the map,'' says artist Wolfgang Staehle, who directs the Thing, a site that exhibits and reviews conceptual art. ''The problem is that few artists have the technological skills to make use of the Web,'' he says.
Wortzel, who teaches art and new media at three of New York's leading art schools, was among the first to span the gap between technology and creativity. Two Macintosh computers produce a steady hum in her fourth-floor walk-up apartment in the East Village. Tradition is close at hand, as one monitor sits atop a dog-eared copy of ''The Great Age of Fresco.''
To make ''The Electronic Chronicles,'' Wortzel scanned reproductions of work by Giotto and other uncopyrighted images into a computer. With an array of software programs, she edited the images and combined them with her own text in a kind of electronic collage.
''I gave up two years of my life to learn this stuff,'' says the former painter. ''Any serious artist must make a commitment to understanding her materials.''
Lately Wortzel's work has taken an unexpected turn. Art journals have been asking her to give interviews and review films in the persona of MUSEleanor, a character who travels freely through time and space in ''The Electronic Chronicles.''
''What began as an experiment in writing and imaging has extended into theater,'' Wortzel says. ''Suddenly I find myself acting.''
As artists try to make sense of such experiences, they are raising questions. Is the Web a new tool for making and displaying art or a revolutionary new art form? Does appropriating an existing image and manipulating it electronically confer authorship? What does it mean to own a work of art that inheres in no object?
There are no easy answers, says artist and entrepreneur Remo Campopiano, who has developed an ambitious site, called artnetweb, that serves as both an art gallery and reference library. ''The Web is a rabbit hole that you fall into,'' he says.
Few sites are more peculiar than Waxweb, the Internet's answer to ''Twin Peaks,'' the experimental 1990-91 TV series. Adapted from a David Blair film called ''Wax or the Discovery of Television Among the Bees,'' Waxweb features thousands of color images and audio files and 500 video clips.
Unlike this article, which progresses in linear fashion from beginning to end, Web sites branch out in countless directions. Click on one of Wortzel's icons, for example, and you enter a labyrinth with seemingly infinite narrative possibilities.
''The funny thing is that 'The Electronic Chronicles' is as low-tech as you can get,'' Wortzel says. ''I started it when the Web's limitations were acute, and that made me focus on content instead of bells and whistles.''
The piece owes as much to experimental fiction as it does to digital technology. Indeed, the Web frequently blurs distinctions between art forms.
''Arctic Circle,'' an Alaskan travelogue by Felix Stephan Huber and Philip Pocock, straddles the not-so-fine line between journalism and performance art. The two artists used a laptop computer and a video camera to record words, images, and sounds of their 5,000-mile trek. En route they posted these multimedia diary entries on the Web.
Proponents say the Web will democratize art by letting artists circumvent traditional gatekeepers. Many artists who have posted their work on the Web revel in their independence from critics, curators, and dealers.
Without the traditional arbiters of quality, some fear that art will suffer. Whether or not that is the case, there is no mistaking that the artists who tend to gravitate toward the Web are often inclined to political or social commentary. Those who regard art as a medium for exploring the subtleties of light and texture, or for expressing the human condition, still opt for traditional materials.
People will not stop applying paint to canvas or setting chisel to stone. ''Art is still art,'' says Mr. Campopiano. ''It's about thinking and putting your guts on the table. The Web is just another way to do it and reach a lot of people.''
Here are addresses for the Web sites mentioned in this story:
* 'The Electronic Chronicles,' by Adrianne Wortzel - http://artnetweb.com/artnetweb/ projects/ahneed/first.html
* The Thing - http://www.thing.net/thingnyc
* artnetweb - http://artnetweb.com
* 'Waxweb,' by David Blair - http://bug.village.virginia.edu
* 'Arctic Circle,' by Felix Stephan Huber and Philip Pocock - http://www.thing.net/~circle/