cellular automata), Andrew Odlyzko (additive cellular automata), Norman Packard (2D cellular automata) and Jim Salem (cellular automaton fluids).

Over the course of the past twenty years I have learned many things relevant to this book from many people. Sometimes I have asked specific questions and got specific answers. Sometimes discussions separated by months or years have gradually made me come to understand something. Sometimes just a single discussion has caused me to learn an important fact or piece of history—or has clarified limitations of some particular field. And sometimes a question asked of me has led me to discover something or to see how to present something better. In all I recall nearly three hundred people who have helped me in these kinds of ways in the past twenty years (this does not include people—especially from the physics community—with whom my main interactions were before 1981, or those with whom my interactions have mostly been about Mathematica or the business of Wolfram Research): Ralph Abraham, Victor Adamchik, Ron Adrian, Guenther Ahlers, Berni Alder, Jan Ambjörn, John Baez, Jim Bailey, Igor Bakshee, Mary Barsony, Andrej Bauer, George Beck, Charles Bennett, Michael Berry, Philippe Binder, Lenore Blum, Manuel Blum, Bruce Boghosian, Enrico Bombieri, Phil Boyland, William Bricken, Bruno Buchberger, Art Burks, David Campbell, John Campbell, Chris Carlson, Pete Carruthers, Forrest Carter, Elise Cawley, Greg Chaitin, Steve Christensen, David Chudnovsky, Gregory Chudnovsky, John Conway, Barbara Cooper, Jack Cowan, Richard Crandall, Jim Crutchfield, Karel Culik, Predrag Cvitanovič, Gautam Dasgupta, Roger Dashen, Martin Davis, Richard Dawkins, David Deutsch, Kee Dewdney, Persi Diaconis, Whitfield Diffie, Freeman Dyson, Paul Erdős, Benson Farb, Doyne Farmer, Mitchell Feigenbaum, Carl Feynman, Richard Feynman, David Finkelstein, Michael Fisher, Mike Foale, Joseph Ford, John Franks, Ed Fredkin, Harvey Friedman, Uriel Frisch, Peter Gacs, Jill Gardner, Laurie Gay, Todd Gayley, Richard Gaylord, Murray Gell-Mann, Roger Germundsson, Etienne Ghys, Don Glaser, Nigel Goldenfeld, Shafi Goldwasser, Beatrice Golomb, Solomon Golomb, Bill Gosper, Peter Grassberger, Alfred Gray, Jeremy Gray, John Gray, Theodore Gray, David Griffeath, Misha Gromov, David Gross, John Guckenheimer, Charlie Gunn, Howard Gutowitz, Hyman Hartman, Jeff Harvey, Brosl Hasslacher, David Hawkins, Gustav Hedlund, Danny Hillis, Pierre Hohenberg, John Holland, John Hopfield, Bernardo Huberman, Alfred Hübler, Dominique d'Humières, Lyman Hurd, Ken Iverson, Raymond Jeanloz, Erica Jen, Leo Kadanoff, Dave Kammeyer, Kuni Kaneko, Stuart Kauffman, Karen Kavanagh, Jerry Keiper, Evelyn Fox Keller, Veikko Keränen, Scott Kirkpatrick, Sergiu Klainerman, Rob Knapp, Don Knuth, Rocky Kolb, John Koza, Bob Kraichnan, Yoshi Kuramoto, Jeff Lagarias, Rolf Landauer, Jim Langer, Chris Langton, Joel Lebowitz, David Levermore, Leonid Levin, Silvio Levy, Steven Levy, Debra Lewis, Wentian Li, Albert Libchaber, David Librik, Dan Lichtblau, Doug Lind, Aristid Lindenmayer, Kristian Lindgren, Chris Lindsey, Ed Lorenz, Saunders Mac Lane, Roman Mäder, Janice Malouf, Benoit Mandelbrot, Norman Margolus, Oleg Marichev, Olivier Martin, Yuri Matiyasevich, John Maynard Smith, Curt McMullen, Hans Meinhardt, Michel Mendès France, Nick Metropolis, John Miller, John Milnor, Marvin Minsky, Don Mitchell, Kim Molvig, John Moussouris, Walter Munk, Jim Murray, Lee Neuwirth, Alan Newell, Mats Nordahl, John Novak, Andrew Odlyzko, Steve Orszag, George Oster, Peter Overmann, Norman Packard, Heinz Pagels, Leonard Parker, Roger Payne, Holly Peck, Hans-Otto Peitgen, Roger Penrose, Alan Perelson, Malcolm Perry, Charlie Peskin, David Pines, Simon Plouffe, Yves Pomeau, Bjorn Poonen, Marian Pour-El, Kendall Preston, Lutz Priese, Ilya Prigogine, Itamar Procaccia, Charles Radin, Tom Ray, Jim Reeds, John Reif, David Reiss, Stanley Reiter, Ken Ribet, Jane Richardson, Ron Rivest, Igor Rivin, Terry Robb, Julia Robinson, Raphael Robinson, Robert Rosen, Gian-Carlo Rota, Lee Rubel, Rudy Rucker, David Ruelle, Jim Salem, Len Sander, Dana Scott, Terry Sejnowski, Rob Shaw, Tim Shaw, Steve Shenker, Bev Sher, Tsutomu Shimomura, Peter Shor, Brian Silverman, Karl Sims, Steven Skiena, Steve Smale, Caroline Small, Alvy Ray Smith, Bruce Smith, Lee Smolin, Mark Sofroniou, Gene Stanley, Ken Steiglitz, Dan Stein, Paul Steinhardt, Adam Strzebonski, Pat Suppes, Gerry Sussman, Klaus Sutner, Noel Swerdlow, Harry Swinney, Bart Taub, David Terr, René Thom, Bill Thurston, Tom Toffoli, Alar Toomre, Russell Towle, Amos Tversky, Stan Ulam, Leslie Valiant, Léon van Hove, Ilan Vardi, Hal Varian, Geerat Vermeij, Gerard Vichniac, Stan Wagon, Bob Wainwright, Bruce Walker, Denis Weaire, Eric Weisstein, Paul Wellin, Caroline Wickham-Jones, Tom Wickham-Jones, Amie Wilkinson, Stephen Willson, Jack Wisdom, Rob Wolff, Alexander Wolfram, Conrad Wolfram, Sybil Wolfram, Lewis Wolpert, Michael Woodford, Larry Wos, Larry Yaffe, Victor Yakhot, Jim Yorke, John Zerolis, Richard Zippel, George Zweig, Helio Zwi. In addition to those with whom I have had direct contact, other individuals have provided input indirectly through my assistants or others (excluding photograph sources listed in the colophon): Bill Beyer, Sheila Blair, Victor Dan, Brent Daniel, Noam Elkies, Peter Falloon, Erich Friedman, Jochen Gerber, Branko Grünbaum, Richard Guy, Michel Janssen, Martin Kraus, Temur Kutsia, Richard Langley, Bernd Löchner, Crista Malick, Brendan McKay, Thomas Scanlon, Rob Scharein, Marjorie Senechal, Marc Sher, David Singmaster, Neil Sloane, Milton Van Dyke, Bob Veroff, Curtis Wilson, Mirek Wójtowicz. Librarians at many institutions—especially the University of Illinois—have often helped my assistants in locating materials. Many individuals at Wolfram Research have also contributed their collective breadth of knowledge on diverse smaller questions.

I began serious development of ideas that eventually led to this book in 1981, and until 1988 I continued to be a member of various academic institutions: California Institute of Technology (Physics Department, 1978–1982), Institute for Advanced Study, Princeton (School of Natural Sciences, 1982–1986), University of Illinois (Center for Complex Systems Research, and Departments of Physics, Mathematics and Computer Science, 1986–1988). I built up successively larger research groups at these institutions, and both the scientific and other members of these groups made a variety of contributions to my work.

In the early to mid-1980s I was a consultant to a number of organizations. The primary ones at which I pursued projects that helped me in formulating issues for this book were Bell Laboratories, Los Alamos National Laboratory and Thinking Machines Corporation. In the period before 1986 a few of my projects received incidental support from various parts of the U.S. government, and I made use of early workstation computers given to me by Sun Microsystems. The MacArthur Fellowship that I received in May 1981 was an important element of personal support, and in fact it was a few months after this award that I made the decision to focus