Selfing dynamics in the rule space of additive cellular automata

Abstract

A unique aspect of additive cellular automata (CA) rules is that the state space on which these rules operate is also the representation space for the rules. Thus, a rule can operate on itself to produce a new rule that is not just its square. This operation will be called selfing, in analogy to reproduction by selfing in Mendelian genetics. This paper explains the properties of the selfing operation on one-dimensional binary-valued additive CA. Results characterizing the selfing transition diagram are derived and some suggestions as to possible applications are presented. The most transparent expression of results is given by representing both rules and states in terms of roots of unity, and this formalism is briefly developed in the initial section.

Keywords:

• additive cellular automata
• self-referential transformations
• state and rule transition diagrams