CHAOS Making a New Science By James Gleick Viking. 352 pp. $19.95

A LOT of the most interesting new work being done in mathematics, physics and biology is tied in with the word chaos. Used by scientists, "chaotic" does not mean "random" so much as it means "purposeful disorder." A chaotic process weaves an intricate cocoon of variation around a simple worm of repetitive rules.

What are some examples of chaos? There's no need to the trot out the slightly bogus quarks and superclusters dear to Big Science; no indeed, chaos theory is about human-scale things like weather, traffic and the heart. One of the classic monographs on chaos theory is The Dripping Faucet as a Model Chaotic System, published in 1984 by a man named Robert Shaw. Shaw actually timed the intervals between tens of thousands of drops from a faucet, massaged the data, and came up with some graphs -- fuzzy horseshoe shaped things, not at all like the random smudges one might expect. A faucet caught right between dripping and dribbling is totally unpredictable without being fully random. It's chaotic.

One's moods are another example of a chaotic system. The slightest thing can change a whole day -- this is what's known as "sensitive dependence on initial conditions." Yet no matter what kind of day you have, you can normally expect to cycle back through your usual range of moods a few days later -- chaos theorists call this "topological transitivity." And -- the third prerequisite for full mathematical chaos -- your moods are coupled to certain built-in biorhythms that foster the dream of achieving a truly metronomic periodicity. Chaos is when something manages to be both simple and infinitely complicated at the same time -- like a person, like the weather, like a dripping faucet.

James Gleick's Chaos is a welcome history and overview of this brand-new subject. One marvels at the amount of legwork that Gleick (a science writer for The New York Times) has done. He seems to have visited everyone in the world who's worked on chaos theory, and his footnotes make reference to every key chaos publication right up through 1987. Gleick's Chaos is a feast, a packed book that will repay many hours of study.

Reading Gleick, one learns that chaos shows up everywhere: in telephone static, in fluid turbulence, in the population models of ecology, and in the orbits of stars flying around and around the galactic center like spirits in an outer circle of Dante's Hell. Chaos! In the words of one psychiatrist, "Is it possible that mathematical health, which is the predictability . . . of this kind of structure, is disease?"

Even the fractals -- those friendly new mathematical forms with the spikiness and detail of physical objects -- are here on a multipage full-color insert. What are fractals doing in a book about chaos? It turns out that a chaotic system can be described in terms of a "strange attractor" consisting of behavior patterns the system is cycling through. And in order for a strange attractor to squeeze a endless amount of confusion into a finite space it has to be an infinitely regressing fractal. Whether not that means anything to you, Peitgen and Richter color plates of the buttock-shaped Mandelbrot set make great centerfold material.

Chaos is still new enough to be hard to write about. While excellent as history and reportage, Gleick's Chaos is a bit weak as popular science -- he never quite comes through with the key explanation that nails it all down. Readers who want a little more detail may want to order copies of some of the disks, books and films distributed by Ralph Abraham's Aerial Press (P.O. Box 1360, Santa Cruz, CA 95061). But the fact that chaos theory is still so new and nebulous is what makes Gleick's book a work capable of generating considerable intellectual excitement, and Chaos could well prove to be something of a scientific best-seller.

Readers who aren't too heavily into actual science may possibly enjoy Gleick's many romanticized descriptions of scientists in action. Right on the second page we have Mitchell Feigenbaum: "His hair was a ragged mane, sweeping back from his wide brow in the style of busts of German composers. His eyes were sudden and passionate. When he spoke, always rapidly, he tended to drop articles and pronouns in a vaguely middle European way, even though he was a native of Brooklyn." This is laying it on a bit thick for the math crowd, but maybe its just the touch needed to reach the masses.

What if a lot of people do get into chaos theory? How might it affect them them? The truth shall set ye free. It's liberating to see oneself as a chaotic system within the larger chaos called society. Before chaos, people naturally assumed that "a system that was visibly unstable, unpredictable, or out of control must either be governed by a multitude of independent components or subject to random external influences." But actually nothing's wrong at all, chaos is health, there's no hope of control, so we can relax and enjoy the show.

Rudy Rucker is a professor of mathematics and computer science at San Jose State University. His recent publications include the cyberpunk novel "Software" and the popular science book "Mind Tools."