I do not know exactly what made me start looking more carefully at simple initial conditions, though I believe that I first systematically generated high-resolution pictures of all the k = 2 , r = 1 cellular automata as an exercise for an early laserprinter—probably at the beginning of 1984. … In the early summer of 1985 I was doing consulting at a startup company called Thinking Machines Corporation, which had developed a massively parallel computer called the Connection Machine that was fairly well suited to cellular automaton simulation. … And in mid-1985, partly in an attempt to find uses for the Connection Machine, I devised a practical scheme for doing fluid mechanics with cellular automata (see page 378 ).

It is also possible to set up emulations where this equality does not hold—and indeed some of the cases listed in the main text and shown in the picture above are of this type.

In general the main way large molecules have traditionally ended up being considered chemically interesting is if they occur in biological systems—or mimic ones that do.

At least formally, general relativity does nevertheless suggest infinite transformations of time in various cases.

Looking at curve (b) on page 135 , however, it does not seem inconceivable that an odd perfect number could exist.

But even when this does not happen, the limiting behavior for small a is still (1/a) d for any nested pattern.

But when the transition is passed, the system does not immediately become completely ordered.

Brittle materials—such as chalk or glass—do not deform significantly before catastrophic failure.

In two kinds of cases, however, this does not happen: one is so-called anomalies, the other interactions with the Higgs field, in which couplings are proportional to mass.

There was an attempt in the 1970s and early 1980s to look directly at the path integral—without doing an expansion in terms of Feynman diagrams. … Even if one assumes that spacetime is in a sense ultimately continuous one can imagine investigating quantum gravity by doing some kind of discrete approximation. … In recent times the most widely discussed have been spin networks—which despite their name ultimately seem to have fairly little to do with the systems I consider.