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So just like for the various kinds of programs that we discussed in the previous chapter , the details of underlying rules again do not seem to have a crucial effect on the kinds of behavior that can occur.
the idea is to do all possible replacements at each step—and then to keep all the possible different sequences that are generated.
Yet now these structures do not just remain fixed, but instead move around and interact with each other in complicated ways.
Do such systems always produce randomness even with simple initial conditions?
The mathematical structure of these systems is nevertheless such that digits further to the left do not affect those shown: at each step the number obtained is effectively reduced modulo 2 n , where n is the width of the picture.
There is no doubt that they do, and as one example I will briefly discuss here what is probably the most obvious feature of essentially all financial markets: the apparent randomness with which prices tend to fluctuate.
It does not, however, conserve the total number of black cells.
The World of Simple Programs The Search for General Features
At the beginning of the last chapter we asked the basic question of what simple programs typically do.
And as I discussed in the previous chapter the process of evolution of a system like a cellular automaton can for example perfectly well be viewed as a computation, even though in a sense all the computation does is generate the behavior of the system.
In cases (a)–(l) the constraints can be satisfied, and the minimal strings which do so are shown.