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For in almost all cases they involve programs whose rules and initial conditions can be specified with perfect precision—so that they work exactly the same whenever and wherever they are run.
And since several of the 256 elementary cellular automaton rules already generate great complexity, just studying a couple of pages of pictures like the ones at the beginning of this chapter should in principle have allowed one to discover the basic phenomenon of complexity in cellular automata.
We have seen in this book many examples of systems where simple sets of rules give rise to highly complex behavior.
The rule 30 cellular automaton provides a particularly clear and good example of intrinsic randomness generation.
But one of the central discoveries of this book is that this is not in fact the case, and that at least if one thinks in terms of programs rather than traditional mathematical equations, then even models that are based on extremely simple underlying rules can yield behavior of great complexity.
And as the pictures on the facing page demonstrate, the same is true even in cellular automata with very simple rules.
But such situations appear to be very much the exception rather than the rule.
application of three-dimensional geometry to very simple underlying rules of growth.
The reversibility of the underlying rules implies that at some level it must be possible to recognize outcomes from different kinds of initial conditions.
So should one conclude from this that the universe is in fact a giant cellular automaton with rules like those of case (c)?