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It is disconcerting to see the degree to which the detailed labor of hundreds of people, and untold hours of computer time, has been reduced to an algorithm. Even though the necessary computations can be realized quite quickly, it is no less impressive to foresee the stupendous amount of time which would be required to obtain certain additional results which initially seem quite simple. For instance, it is out of the question to use the same approach directly to calculate any structures of period 2, much less gliders and space ships which require period 4.

Much of the activity reported in Wainwright's newsletter[8] involved tracking the evolution of diverse small figures, a byproduct of which was a gradually increasing catalog of small still lifes. Many of them grouped themselves into families, whose general structure could be readily perceived, and many people seem to have become quite skilled at designing still lifes and other predictable patterns. Moreover, after having reviewed large collections of still lifes, one develops an eye for flaws and a feeling for what constitutes a proper still life. Which implies that there must be some pattern present which can be recognized.

Golomb's book[4] on shift register sequences disseminated the use of de Bruijn diagrams to characterize long sequences of overlapping symbols, although an application to automata does not seem to have been published until Wolfram's article[9] in 1984. Nowadays they can be seen as a tool for quickly obtaining the personalities of arbitrary automata, subject to the limitations imposed by exponential growth with respect to any of the parameters involved---dimension of the automaton, length of the period, number of states, and so on. Perhaps an even more elaborate theory of higher dimensional de Bruijn diagrams will eventually result.



Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx