Semi-totalistic Automata

Abstract

In view of how tractable linear rules turn out to be, one is encouraged to investigate similar questions for more general rules. A natural next step is to make the next state of a center cell depend, not linearly on the full local distribution of neighboring cells, but rather on the their density and, possibly, its own state. For instance, under a majority rule for an elementary celullar automaton the center cell polls its neighbors for a state and goes with the majority (ties are broken arbitrarily by the center cell, for instance by kee** its current state). These rules are called semi-totalistic. In the particular case of elementary automata, it is necessary to reduce this total count to a binary value. The simplest way to achieve this reduction is to set up a minimal threshold value for the count to become 1.

Article Note

Aye on the shores of darkness there is light, And precipices show untrodden green, There is a budden morrow in midnight, There is a triple sight in blindness keen.

John Keats