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scientific papers are Hao Bai-Lin, Chaos (Singapore: World Scientific, 1984) and Predrag Cvitanović, Universality in Chaos (Bristol: Adam Hilger, 1984). Their selections overlap surprisingly little; the former is perhaps a bit more historically oriented. For anyone interested in the origins of fractal geometry, the indispensable, encyclopedic, exasperating source is Benoit Mandelbrot, The Fractal Geometry of Nature (New York: Freeman, 1977). The Beauty of Fractals, Heinz-Otto Peitgen and Peter H. Richter (Berlin: Springer-Verlag, 1986), delves into many areas of the mathematics of chaos in European-Romantic fashion, with invaluable essays by Mandelbrot, Adrien Douady, and Gert Eilenberger; it contains many lavish color and black-and–white graphics, several of which are reproduced in this book. A well-illustrated text directed at engineers and others seeking a practical survey of the mathematical ideas is H. Bruce Stewart and J. M. Thompson, Nonlinear Dynamics and Chaos (Chichester: Wiley, 1986). None of these books will be valuable to readers without some technical background.

In describing the events of this book and the motivations and perspectives of the scientists, I have avoided the language of science wherever possible, assuming that the technically aware will know when they are reading about integrability, power-law distribution, or complex analysis. Readers who want mathematical elaboration or specific references will find them in the chapter notes below. In selecting a few journal articles from the thousands that might have been cited, I chose either those which most directly influenced the events chronicled in this book or those which will be most broadly useful to readers seeking further context for ideas that interest them.

Descriptions of places are generally based on my visits to the sites. The following institutions made available their researchers, their libraries, and in some cases their computer facilities: Boston University, Cornell University, Courant Institute of Mathematics, European Centre for Medium Range Weather Forecasts, Georgia Institute of Technology, Harvard University, IBM Thomas J. Watson Research Center, Institute for Advanced Study, Lamont-Doherty Geophysical Observatory, Los Alamos National Laboratory, Massachusetts Institute of Technology, National Center for Atmospheric Research, National Institutes of Health, National Meteorological Center, New York University, Observatoire de Nice, Princeton University, University of California at Berkeley, University of California at Santa Cruz, University of Chicago, Woods Hole Oceanographic Institute, Xerox Palo Alto Research Center.

For particular quotations and ideas, the notes below indicate my principal sources. I give full citations for books and articles; where only a last name is cited, the reference is to one of the following scientists, who were especially helpful to my research:

Günter Ahlers

F.Tito Arecchi

Michael Barnsley

Lennart Bengtsson

William D. Bonner

Robert Buchal

William Burke

David Campbell

Peter A. Carruthers

Richard J. Cohen

James Crutchfield

Predrag Cvitanović

Minh Duong-van

Freeman Dyson

Jean-Pierre Eckmann

Fereydoon Family

J. Doyne Farmer

Mitchell J. Feigenbaum

Joseph Ford

Ronald Fox

Robert Gilmore

Leon Glass

James Glimm

Ary L. Goldberger

Jerry P. Gollub

Ralph E. Gomory

Stephen Jay Gould

John Guckenheimer

Brosl Hasslacher

Michel Hénon

Douglas R. Hofstadter

Pierre Hohenberg

Frank Hoppensteadt

Hendrik Houthakker

John H. Hubbard

Bernardo Huberman

Raymond E. Ideker

Erica Jen

Roderick V. Jensen

Leo Kadanoff

Donald Kerr

Joseph Klafter

Thomas S. Kuhn

Mark Laff

Oscar Lanford

James Langer

Joel Lebowitz

Cecil E. Leith

Herbert Levine

Albert Libchaber

Edward N. Lorenz

Willem Malkus

Benoit Mandelbrot

Arnold Mandell

Syukuro Manabe

Arnold J. Mandell

Philip Marcus

Paul C. Martin

Robert M. May

Francis C. Moon

Jürgen Moser

David Mumford

Michael Nauenberg

Norman Packard

Heinz-Otto Peitgen

Charles S. Peskin

James Ramsey

Peter H. Richter

Otto Rössler

David Ruelle

William