General (4,1) automata

Although numerous specialized effects result from mixing all the planes on a CAM board, studying the simplest classes of automata remains one of the major applications of the board; nor should it be forgotten that knowledge of the elementary constituents facilitates the analysis of composite automata.

With its present layout, the most complicated elementary automata that can reside within a half-CAM are those with a (2,1) Moore neighborhood, requiring a table with 512 binary entries, and those with the (4,1) von Neumann neighborhood, requiring 1024 quaternary entries. Of course, a (3,1) von Neumann automaton with a 243 entry trinary table could be accommodated as a special case of the (4,1) automaton, but no space would be saved thereby, either in the bitplanes or in the tables.

The size of their tables makes it difficult to deal with general automata, leading to two alternatives. Many simplifications (such as totalistic rules) have fewer parameters, allowing the full table to be generated without the user's active participation. The other is to look for forms of presentation which will offer increased understanding of the process of editing the rule set, or at least make it more systematic.

Maybe there is a third alternative, which is simply to accept a large table as a legitimate object and to learn how to deal with it. As required, facilities can be added to CAMEX to save rule tables on disk, as well as to recover them.

One way for a table to arise is from a CAMEX editing session, wherein a rule is built up neighborhood by neighborhood while experimenting with trial evolutions. But the table could also be constructed by another program, or copied from somewhere.

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