Table of transitions
Any design can be accomplished by hand using paper and pencil, a procedure quite prone to mistakes. Options which have been added to both the line editor and the rule editor in will render mechanical assistance. Transitions can be marked, evolution can be evaluated generation by generation, and account can be kept of the transitions which have already been defined relative to those which are still available for assignment.
Fortunately, this example yielded a straightforward design, its principal objectives having been met before any significant choices had to be made. Given the basic style, counting and carrying have unique solutions; the selection of the four pairs comprising the glider gun was somewhat more arbitrary, although we knew that the glider could only be exposed on the left wall once per cycle, and that the other two states form stable walls.
Still, were the design to be pursued to its ultimate details, most of the work would be done in harmonizing combinations which would occur very rarely, supposing that the original intentions of the design were to be respected in choosing applications. Finishing of these details could require a tremendous amount of backtracking, making mechanical assistance imperative, and requiring its eventual incorporation in the design process.
In any event, the following table summarizes all the transitions. Those defined at stage 14, or accompanied by a dot indicating that they are still unresolved, are subject to revision by anyone seeking the ultimate in perfection. Each neighborhood is accompanied by its image and, within parentheses, the stage at which it first appeared.
Table 2: Transition table for a binary counter.
Realizing that both the body of the counter and the glider gun can be sketched in crude form by relatively few transitions gives some idea of how common these structures must be among automata in general. The leading edge of whatsoever glider determines its principal characteristics---for example, its velocity of propagation---just as the boundaries between a still life and a quiescent region break the field up into stable domains. Relatively few transitions establish the simplest gliders or boundaries, making them proportionately common phenomena. Consequently they should be among the first characteristics to be checked out when examining and creating a new rule.
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx