**
**

Some images on the back jacket of Stephen Wolfram's 1,197-page tome, "A New Kind of Science," are familiar: a splash of liquid, jets of gas, sea anemone, ancient mosaics and mollusk shells. But others become understandable only after working through ideas in this much-awaited book: spindly sketches of leaves and snowflakes, a baroque lacework of light, schematic diagrams that waver under the gaze.

Many of these images, created by Mr. Wolfram, are ghostlike reductions of familiar objects, skeletal representations of processes that may lie beneath natural forms. And they were produced during a decade of work that was kept hidden from professional scrutiny.

Now Mr. Wolfram is finally publishing his work, and his claims surpass the most extravagant speculation. He has, he argues, discovered underlying principles that affect the development of everything from the human brain to the workings of the universe, requiring a revolutionary rethinking of physics, mathematics, biology and other sciences. He believes he has shown how the most complex processes in nature can arise out of elemental rules, how a wealth of diverse phenomena — the infinite variety of snowflakes and the patterns on sea shells — are generated from seemingly trivial origins.

Conducting experiments on a computer, where he says he has logged 100 million keystrokes in the last 10 years, Mr. Wolfram wrote simple programs that generated odd and intricate patterns to test his ideas about complexity. He then tried to imitate designs found in nature. He argues that natural phenomena can be explored as if they were, in fact, computer programs, their evolution and behavior the products of intricate calculations.

"I have discovered vastly more than I ever thought possible," Mr. Wolfram writes in the book's preface, "and in fact what I have done now touches almost every existing area of science, and quite a bit besides."

These might seem the claims of a semimystical scientific crank. After all, the book is being published (on Tuesday) not by a university press but by Mr. Wolfram's own company (Wolfram Media Inc.), and he has insisted on secrecy in a scientific world used to peer review and public conferences. But secrecy and grandiosity have also accompanied major scientific works .

Terrence Sejnowski, who directs the Computational Neurobiology Laboratory at the Salk Institute for Biological Studies in La Jolla, Calif., has found Mr. Wolfram's work useful for designing computer simulations of nerve cells and synapses. He has called Mr. Wolfram "the smartest scientist on the planet."

Mr. Wolfram, who was born in Britain, published his first paper on particle physics in 1975 at age 15, and obtained a doctorate at Caltech at 20 (where Richard Feynman called him "astonishing"). He won a MacArthur Foundation Fellowship at 21, reshaped the ways in which complex phenomena (like the movements of fluids) were analyzed before he was 26, founded an institute for the study of complexity at the University of Illinois, and then left academic life and research science, starting a software company, Wolfram Research Inc., in 1987. His main commercial product, a program called Mathematica, has become an international standard, used as a mathematical tool by over a million scientists and students and engineers in areas ranging from medical research to the analysis of weather.

Mr. Wolfram freely confesses to a high opinion of his accomplishments. In a recent interview, he explained that if he were more modest he would be less clear and less successful. "Ultimately," he said of his book, "confidence is necessary in order to undertake a project of this size." Its goal is to change the very direction of scientific research. He ranks one of his discoveries about complexity among the most important "in the whole history of theoretical science."

But because Mr. Wolfram has been so secretive, he has shown his work only to a small circle of selected colleagues. Gregory J. Chaitin, a mathematician at IBM Watson Research Center in Yorktown Heights, N.Y., for example, who has read the book, said in an interview that he was convinced of its importance but anticipated controversy: "Stephen has gone out on a limb. He is proposing a paradigm shift. A new twist on everything." It will take months, even years, before all the thorough, independent professional assessments are in, which should not be surprising given Mr. Wolfram's undertaking.

He really is proposing, as the book's title puts it, a "new kind of science." He wants to displace the projects and theories and priorities that now characterize academic science. And he refuses to be limited by disciplinary boundaries or by the assertions of experts in other fields. "No doubt," he writes, "this book will draw the ire" of some of them. "I think I was a somewhat brash teenage scientist," Mr. Wolfram said, adding that he still seems to affect people the same way.

As a colleague once put it, Mr. Wolfram has "stepped on a lot of toes." Tensions arose in many institutional settings before he set out on his own. In the early 1980's, there was even a court battle with Caltech over ownership of computer software designed by Mr. Wolfram. In addition, Mr. Wolfram noted, when he began his work on complexity he confidently expected others to follow through on his suggestions; instead, he bluntly said, without his leadership the field did "horribly, horribly." Such frustrations, he explained, eventually convinced him to design an alternative scientific career, founding his own company and pursuing his interests without any need for grants or support.

This independence is even reflected in the book's style. It requires, Mr. Wolfram writes, "no specialized scientific or other knowledge to follow." Mathematical formulas are eliminated; illustrations predominate; professional prose is avoided.

His theory developed out of a series of elementary computer experiments he conducted in the early 1980's. He was examining the way simple computer programs can generate shaded patterns on grids composed of square cells. A computer would be given a row of cells, some black, some white, along with a set of simple rules that determine how succeeding lines of shaded cells are to be generated. Such programs have been called "cellular automata."

As one might expect, simple rules generally yield simple patterns. But Mr. Wolfram found one rule for generating a cellular automaton that yields no clear pattern at all. Its appearance is bizarre, unpredictable, seemingly chaotic. No one, Mr. Wolfram writes, could have expected this. Complexity was thought to arise only out of very complex rules; here it is generated out of simplicity.

Such cellular automata are at the heart of this book, for Mr. Wolfram argues that many complex processes — the movements of a fluid, the shapes of leaves, the patterns on a mollusk shell — can, in fact, be modeled by simple programs like cellular automata. Such elementary programs, he suggests, can even be used to explain the nature of space and time or outline the vagaries of visual perception. Existing mathematics and physics, Mr. Wolfram argues, are inadequate to the task.

Here is where matters get quite difficult very fast. Not only can complex designs and processes arise out of the simplest of rules, but, Mr. Wolfram asserts, simple rules actually lie behind the most sophisticated processes in the universe. Indeed, the universe itself, he argues, is generated by such rules. He presents an example of one cellular automaton program that produces such sophisticated patterns that it can act like a powerful computer. The details are highly technical, but this automaton can actually replicate other processes and patterns just as a computer can be turned into a word-processor one minute and a game machine the next. It has what are called "universal" properties.

Hypothetically, the movement of cigarette smoke in the air could be mirrored by such a seemingly simple cellular automaton; so could the processes of the human brain. In fact, such powerful "computers," Mr. Wolfram says, are far more plentiful, even in the natural world, than has ever been thought. Moreover, he argues that all universal computing systems are equivalent; no calculating machine can be more powerful, no computer more sophisticated than the cellular automaton Mr. Wolfram describes. This insight alone, he claims, "has vastly richer implications" than "any single collection of laws in science."

And indeed, this principle, as asserted by Mr. Wolfram, leads to a startling conclusion. Scientists are accustomed to analyzing some systems by discovering abstract principles that can describe their behavior. Kepler's laws, for example, can predict and describe the motion of the planets. But some extraordinarily complex processes — like, perhaps, the curl of cigarette smoke — cannot be encompassed by such a law; for that law would require one "universal" computational system to be more powerful than another.

So all we can do in such cases is discover the simple rules that give birth to the complexity, the rules that act like the striking of the match before smoke begins to rise. Everything else — the position and density of smoke at a particular time and under certain conditions — can be found only by "experiment": the process must run its course. There are limits to the powers of science to generalize and predict.

Mr. Wolfram spins out elaborate speculations based on these ideas — suggestions about free will, the structure of space, the nature of mathematics. "There is so much in the book," Mr. Sejnowski said, "that it will be years, literally years, before people assimilate it." Meanwhile, reactions to Mr. Wolfram, he believes, will be "all over the map."

Mr. Wolfram is sanguine: "I am quite certain this is going to work. I have never deluded myself before."