And indeed it is my strong suspicion that for essentially all purposes the only reasonable model for important new features of organisms is that they come from programs selected purely at random. So does this then mean that there can never be any kind of general theory for all the features of higher organisms? … Seeing in earlier chapters of this book all the diverse things that simple programs can do, it is easy to be struck by analogies to books of biological flora and fauna.

[No text on this page] Evolution of cellular automata with a sequence of different possible rules, starting in all cases from a single black cell.

But what all the rules have in common is that they involve replacing one black square by two or more smaller black squares. And with this kind of setup, it is ultimately inevitable that all the patterns produced must have a completely regular nested structure. … And the result of this has been that in traditional fractal geometry the idea of interaction between elements is not considered—so that all patterns that are produced have a purely nested form.

particular string, then at each successive step one applies all possible transformations, so that in the end one builds up a whole network of connections between strings, as in the pictures below. … One might at first assume that any theorem that is easy The result of applying the same transformations as on the facing page —but in all possible ways, corresponding to the evolution of a multiway system that represents all possible theorems that can be derived from the axioms.

In all cases where the constraints can be satisfied at all, a simple repetitive pattern nevertheless suffices.

One might think, for example, that the fact that all the cells in a cellular automaton follow exactly the same rule would mean that in pictures like the last few pages [ 32 , 33 , 34 , 35 , 36 , 37 , 38 ] all cells would somehow obviously be doing the same thing. … And what makes this possible is that even though individual cells follow the same rule, different configurations of cells with different sequences of colors can together produce all sorts of different kinds of behavior. Looking just at the original cellular automaton rule one would have no realistic way to foresee all of this.

instructions one can get all sorts of complex behavior is similar to the phenomenon we have seen in cellular automata. … Yet when we ran them we ended with patterns so complex that they seemed to defy any simple description at all. … We have seen so far only a few examples, all in cellular automata.

For if all that is left at the end are a few simple structures, how can there be enough information to go backwards and reconstruct the initial conditions? The answer is that one has to consider not only the stationary structures that stay in the middle of the system, but also all various small structures that were emitted in the course of the evolution. … The result is that the evolution one sees can be intrinsically not reversible, so that all of the various forms of self-organization that we saw earlier in this book in cellular automata that do not have reversible rules can potentially occur.

specific process one can apply it to a piece of raw data, and then see how the results compare with those obtained from all possible sequences. If the process is sufficiently simple then by using traditional mathematics one can sometimes work out fairly completely what will happen with all possible sequences. … And indeed this is what I have found for all simple cellular automata that I have searched.

In its typical form this procedure works by dropping all vowels and grouping together letters like "d" and "t" that sound similar, with the result that at least in some approximation the only features that are kept are ones that make a difference in the way a word sounds. … In many respects one of the primary goals of all forms of perception and analysis is precisely to pick out those features of data that are considered relevant, and to discard all others. … In actual brains it is fairly clear that input received by all the various sensory systems is first processed by assemblies of nerve cells that in effect extract certain specific features.