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And thus, for example, given a somewhat complicated visual image—say of a face or a cellular automaton pattern—we can often not even immediately recognize similarity to the same image turned upside-down.
A description based on output from a cellular automaton rule that one has never seen before is thus for example not likely to be useful.
Indeed, from our discussion in the previous chapter , we already know that among the 256 very simplest possible cellular automaton rules at least rule 110 and three others like it are universal.
One could imagine doing much as I did early in this book and successively looking at every possible rule for some type of system like a cellular automaton.
And so, for example, I suspect that it does not take a cellular automaton nearly as complicated as the one on page 767 for it to be an NP-complete problem to determine whether initial conditions exist that lead to particular behavior.
whether, say, a particular pattern would ever die out in the evolution of a given cellular automaton.
The functions are numbered like 2-neighbor analogs of the cellular automaton rules of page 53 .
But what I have shown in this book is that this is not the case, and that in fact a vast range of systems—including ones with very
A two-dimensional cellular automaton that exhibits an almost trivial form of self-reproduction, in which multiple copies of any initial pattern appear every time the number of steps of evolution doubles.
For my discoveries imply that whether the underlying system is a human brain, a turbulent fluid, or a cellular automaton, the behavior it exhibits will correspond to a computation of equivalent sophistication.
2D fluids
The cellular automaton shown in the main text is purely two-dimensional.