Basins of Attraction of Cellular Automata Based Associative Memory and Its Rule Space

In this paper, we analytically establish two important observations reported in (P. Maji et al., 2003) and (N. Ganguly et al., 2002) - the nature of the basins of attraction of a special class of non-linear cellular automata (CA), referred to as generalized multiple attractor CA (GMACA) (P. Maji et al., 2003); and the characteristics of the evolved GMACA rule space (N. Ganguly et al., 2002). Characterization of the basins of attraction of the GMACA ensures the sparse network of CA as a powerful pattern recognizer for memorizing unbiased patterns. An in-depth analysis of GMACA rule space has established that more heterogeneous CA rules are capable of executing complex computation like pattern recognition. That is, the rule space of the pattern recognizing CA lies at the edge of chaos