Yet cellular automata and most of the other programs that we have discussed involve only discrete elements.

The only configurations that ultimately satisfy the constraints are all white and all black.

And only when natural selection is not crucial, therefore, will biological systems be

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 in the end it seems that even though only a very small fraction of possible systems have the property of being reversible, such systems can still exhibit behavior just as complex as one sees anywhere else.

And it turns out that in this particular case only very simple repetitive behavior is ever obtained.

One fairly simple scheme, illustrated on the facing page , allows only a single replacement to be performed at each step, and picks the location of this replacement so as to affect the least recently updated nodes.

And the cell in the visual cortex will then respond only if enough of its inputs are positive, corresponding to a specific pattern being present in the image. … Responses to two sample images of cells sensitive to the 2×2 template shown on the bottom left. … Such responses occur whenever the 2×2 template on the left appears, corresponding to the presence of a vertical black edge.

But at the end of that section I showed that the fairly simple procedure of two-dimensional pointer Examples of all the distinct repetitive patterns that can be formed from arrays of 2×2 and 3×3 blocks. … Page 215 shows patterns obtained in systems based on constraints in which one effectively requires that only certain blocks or sets of blocks occur.

And potentially therefore our lack of higher forms of perception and analysis might in the end have nothing to do with any difficulty in implementing such forms, but instead may just be a reflection of the fact that we only have enough context to make descriptions of data useful when these descriptions are fairly close to the ones we get from our own built-in human methods of perception.