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And in this system, unlike all others before it, no repetitive pattern is possible; the only pattern that satisfies the constraint is the non-repetitive nested pattern shown in the picture.
cellular automata with rules as simple as the ones we have been using these three forms of behavior would be all that we could ever get.
But it is never possible to eliminate absolutely all interaction with the environment.
In the detailed behavior of the various localized structures that separate these domains of repetitive behavior there is all sorts of complexity.
For I believe that all these types of rules in some sense probably already have too much structure built in.
These networks can be continued forever, and all have the property of being homogeneous, in the sense that every node has an environment identical to every other node.
The pictures on the facing page show what happens if at each step one allows not just a single replacement, but all replacements that do not overlap.
It is also easy to extend block-based encoding to two dimensions: all one need do is to assign codewords to two-dimensional rather than
Examples of one-dimensional pointer-based encoding applied to patterns produced by cellular automata.
In this section we will discover that in fact almost all of the systems that we considered in the previous section —and in Chapter 3 —have the same capabilities.
(One sees many branches in the fossil record—such as organisms with dominant symmetries other than fivefold—but all seem to have the same ancestry.)
… But with the advent of widespread computer simulations in the 1980s it became clear that all sorts of features normally associated with life were actually rather easy to obtain.