in prices in a sense just reflections of random changes going on in the outside environment. … And knowing this, one might then think that perhaps random fluctuations are just an inevitable feature of the way that prices adjust to their correct values. … It is sometimes claimed that it is somehow inevitable that markets must be random, since otherwise money could be made by predicting them.

But the examples on the second of the next two pages instead start with the number π /4 —which has a seemingly random digit sequence. … But on the second page , it yields numbers whose sizes continually vary in a seemingly random way. … And this means that over the course of the evolution of the system, digits further to the right in the original number will progressively end up all the way to the left—so that insofar as these digits show randomness, this will lead to randomness in the sizes of the numbers generated.

And what we see immediately from these pictures is that while some systems exhibit exactly the kind of randomization implied by the Second Law, others do not. … The picture on page 456 shows what happens if one starts rule 37R with a single small region of randomness. And for a while what one sees is that the randomness that has been inserted persists.

there will be an additional source of randomness: the arbitrariness of the path corresponding to the history that we have experienced. In many respects this randomness is similar to the randomness from the environment that we discussed at the beginning of Chapter 7 . … And indeed I would not expect that observations of randomness could ever reasonably be used to show that our universe is part of a multiway system.

One general strategy is to add randomness, so that in essence one continually shakes the system to prevent it from getting stuck. … The procedure at the top of the facing page already in a sense involved randomness, for it picked a square at random at each step. … A random square is again picked at each step.

At first glance, these images do in some respects look more random. … And knowing such a hierarchy, one should be able to produce images that in a sense seem as random as possible to us. … Examples of images that approximate perfect randomness.

The definition of randomness that we discussed in the previous section was based on the failure of the second of these two functions. … In everyday language, the terms "complexity" and "randomness" are sometimes used almost interchangeably. And for example any of the three pictures at the top of the next page could potentially be referred to as either "quite random" or "quite complex".

random, then progressively modifies the pattern so as to make it closer to satisfying the constraints. As a specific example consider taking a series of steps, and at each step picking a square in the array discussed above at random, then reversing the color of this square whenever doing so will not increase the total number of squares in the array that violate the constraints. … The procedure starts with a randomly chosen pattern, then at each step picks a square in the pattern at random, and reverses the color of this square whenever doing so does not increase the total number of squares in the pattern that violate the constraints.

And the pictures below show for example cases where the behavior inside each domain is quite random. Instead of following simple straight lines, the boundaries of these domains now execute seemingly random walks. … But what we Examples involving domains containing apparent randomness.