And if one identifies a feature—such as repetition or nesting—that is common to many possible systems, then it becomes inevitable that this feature will appear not only when intelligence or mathematics is involved, but also in all sorts of systems that just occur in nature.

And indeed my guess is that the essential features of all sorts of intricate structures that are seen in living systems can actually be reproduced with remarkably simple rules—making it for example possible to use technology to repair or replace a whole new range of functions of biological tissues and organs.

(Especially in antiquity, all sorts of seemingly random phenomena have been used as a basis for fortune telling.) … There are all sorts of situations where in the absence of anything better it is good to use randomness. … Examples include message routing in networks, retransmission times after ethernet collisions, partitionings for sorting algorithms, and avoiding getting stuck in minimization procedures like simulated annealing.

And in fact the 4D vacuum Einstein equations are already a sophisticated set of nonlinear partial differential equations that can support all sorts of complex behavior. … If anisotropy is present, however, then there can be all sorts of solutions—classified for example as having different Bianchi symmetry types. … (Numerical simulations often show all sorts of complex behavior—but in the past this has normally been attributed just to the approximations used.

Given the original list s and the complete prime implicant list p the so-called Quine–McCluskey procedure can be used to find a minimal list of prime implicants, and thus a minimal DNF: QM[s_, p_] := First[Sort[Map[p 〚 # 〛 &, h[{}, Range[Length[s]], Outer[MatchQ, s, p, 1]]]]] h[i_, r_, t_] := Flatten[Map[h[Join[i, r 〚 # 〛 ], Drop[r, #], Delete[Drop[t, {}, #], Position[t 〚 All, # 〛 ], {True}]]] &, First[Sort[Position[#, True] &, t]]]], 1] h[i_, _, {}] := {i} The number of steps required in this procedure can increase exponentially with the length of p .

All sorts of schemes have been invented for getting unbiased output from such systems, and acceptable randomness can often be obtained at kilohertz rates, but obvious correlations almost always appear at higher rates.

And in fact, intuition from traditional science and mathematics has always tended to suggest that unless one adds all sorts of complications, most systems will never be able to exhibit any very relevant behavior.

And equipped with Mathematica I began to try all sorts of new experiments.

But the pictures on the next two pages [ 29 , 30 ] show that nothing of the sort happens.

But superimposed on this is all sorts of elaborate and seemingly quite random behavior.