Appendix 1. Frequently used local rules

This appendix presents the nomenclature conventions (A 1) for local rules, frequently used local rules (A 2) and some rules invoked in the discussion of Turing equivalence of cellular automata.

The denomination of rules introduced by Wolfram [8] refers to 3-bit Boolean functions. Each function is designated by the configuration in the look-up table, read in reverse (hence, in this context, the look-up table is drawn starting with the last value). In A 1, the look-up table of the


A 1. Each 3-bit rule is designated by the value in the look-up table.


A 2. Frequently used local rules for random number generation with linear cellular automata.

rule 30 is given. Table 2 gives the specific configuration in the look-up table for some of frequently used rules cited in this paper, according to the references list.

In the basic rule in the Game of Life binary, two-dimensional cellular automata, the significance of 0 and 1 is that a cell is dead or alive. With a Moore neighborhood, the rule can be described as follows:


In the Game of Life, there are several patterns that persist for ever, either in a dynamic or static manner. For instance, gliders are patterns that are moving. The demonstration of the Turing equivalence for the Game of Life involves flows of gliders that perform logic functions.

Rule 110, in linear cellular automata (binary code 01101110), is a class IV rule in Wolfram's taxonomy and, like Life, is Turing equivalent.
