The subject of cellular automata has passed through several stages of evolution during the fifty or so years during which it may be thought to have existed. It is interesting to see what has been accomplished during this time, and not only to speculate as to what remains to be done but also to wonder to what degree the subject has applications, and how successful it will be in meeting the expectations which may be held for it.
If an automaton is supposed to be a mechanism capable of performing intricate tasks or exhibiting complex behavior, the concept is surely as old as antiquity; but it was not until the mastery of electricity at the end of the last century that really delicate and subtle constructs could be imagined. Far beyond that, it required an advanced degree of electronics, and even of microelectronics in the form of reliable vacuum tubes, transistors, and nowadays integrated circuits, before truly elaborate automata could become a reality.
For this reason, the innovative ideas of Warren McCulloch and Walter Pitts[50] and the designs of John von Neumann[53] are more properly considered to be the foundations of automata theory than, say, Charles Babbage's[3] proposal for his difference engine or the more advanced analytical engine which made use of ideas taken from the Jacquard loom. As it is, there is a wide variety of sources from which to choose, whatever one's point of view. Little of this will be taken into further account here, but for those interested there are excellent references which can be consulted[60,2,30,26].
McCulloch and Pitts' investigations concerned the possibility of constructing a model of mental processes. While derived from their knowledge of the physiology of nervous systems, their model was intended mostly to reflect characteristics such as the connectivity of the neural net or the interactions in Boolean terms of signals propagating through it. Neither the strict form of the signals, nor the material composition of the neurons were considered to be primary issues.
In similar fashion, von Neumann thought of different models, some of them quite physical, through which his plans for automatic construction could be realized. Nevertheless, as is quite the custom among mathematicians, the abstract approach proved to be the formulation which seemed best to capture the central ideas.
From such a beginning voluminous results have followed, both in the form of mathematical theorems and in the design of specific circuits, all of which have been duly recorded in the scientific literature. Cellular automata achieved substantial popular notoriety when John Conway took up the subject[16] and Martin Gardner reported one of his most interesting discoveries in Scientific American [28]. The evangelical efforts of Stephen Wolfram[70] have given a whole new dimension to the topic in recent years.