Probabilistic menu

The probabilistic menu contains all the options pertaining to the statistics of automaton evolution. The greatest variation between programs results form differences in graphical treatment of different sets of probabilities.

For binary automata, only one probability is required, since the probability of the other state is the complement of the first. Consequently, simple two- dimensional graphs suffice to show how probability changes from one generation to another; for instance through mean field curves. Binary automata are also simple enough that contour maps can represent block probabilities for pairs.

Trinary automata have two independent probabilities, for which contours in triangular coordinates suffice; beyond three states simplices of at least three dimensions are required.

Stereopairs showing sections through a pyramid can be used to display the probabilities of quaternary automata. Since a certain amount of practice and training are necessary to visualize stereopairs, or else special optical equipment, many people fail to appreciate stereopairs. Other representations are possible, including dynamic displays with rotation, but they do not form part of the LCAU program set.

Beyond four states it becomes increasingly difficult to represent probabilities, although most of the programs contain vestiges of the quaternary treatment. These are due to a certain laziness in programming, and will gradually be eliminated from the programs.





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