Many people have contributed in various ways to the material presented here. For specific suggestions I thank: Persi Diaconis, Carl Feynman, Richard Feynman, Shafi Goldwasser, Peter Grassberger, Erica Jen, and John Milnor.
For discussions I thank: Lenore Blum, Manuel Blum, Whit Diffie, Rolf Fiebrich, Danny Hillis, Doug Lind, Silvio Micali, Marvin Minsky, Andrew Odlyzko, Steve Omohundro, Norman Packard, and Jim Reeds.
For help with computational matters I thank: Keira Bromberg, Bill Gosper, Don Mitchell, Bruce Nemnich, Holly Peck, Jim Salem, Tsutomu Shimomura, Steve Strassmann, and Don Webber.
The computer mathematics system SMP  was used for some of the calculations. I thank the Science Office of Sun Microsystems for the loan of a SUN workstation on which most of the graphics and many of the calculations were done. And finally I thank Thinking Machines Corporation for the use of a prototype Connection Machine computer , without which much more about the cellular automaton of Eq. (3.1) would still be unknown.
Note added in proof. Eq. (3.1) can also be used to generate efficiently a key sequence for stream encryption .