NSRT diagram for identification of SACA and TACA rules in null-boundary

Abstract

This work reports characterization of one-dimensional null-boundary cellular automata (CA) rules in 3-neighborhood. The outcome of this characterization is the identification of CA rules that are the probable candidates for producing single length cycle attractor (fixed point). It targets synthesis of CA with only one fixed point (referred to as the single length cycle single attractor CA (SACA)) and the CA with only two fixed points (referred to as single length cycle two attractors CA (TACA)) for arbitrary length. A tool referred to as Next State RMT Transition Diagram (NSRTD) is developed to identify the fixed points as well as the cycles, involving multiple states (multi-length cycles) of a CA. The NSRTD provides the theoretical basis to search for the rules that form SACA and TACA, for all lengths, in null-boundary.