(Page 0339) they become increasingly common. The pictures on the next page show two examples -- the second corresponding to a rule that we saw in a different context at the ...

(Page 0343) 20×20 array this number is larger than the total number of particles in the universe. So it seems quite inconceivable that systems in nature could ever carry out ...

(Page 0354) It is common for uniform behavior to be quite independent of initial conditions or other input to a system. But sometimes different uniform behavior can be ...

(Page 0449) measurements, so that the amount of information needed to pick out a single arrangement is essentially the length in digits of one such number. The pictures below ...

(Page 0477) Each of these networks is at the lowest level just a collection of nodes with certain connections. But the point is that the overall pattern of these connections ...

(Page 0504) Uniqueness and Branching in Time If our universe has no built-in global clock and no construct like an active cell, then it is almost inevitable that at the ...

(Page 0525) Elementary Particles There are some aspects of the universe -- notably the structure of space and time -- that present-day physics tends to assume are continuous. ...

(Page 0565) But ultimately there is a limit to the degree of compression that can be obtained with this method. For even in the very best case any block of cells in the input ...

(Page 0586) The answer, it seems, is surprisingly simple: we readily recognize exact or approximate repetition at definite frequencies, and essentially nothing else. So if we ...

(Page 0611) than pairs. And once again the numbers appear as coefficients, but now in the expansion of powers of 1+x+x ^ 2 rather than of 1+x . So is there an explicit ...