On the study of cellular automata on modulo-recurrent words

In this paper, we study some class of cellular automata (CA) preserving modulo-recursive, stability by reflection and richness called stable cellular automata (SCA). After applying these automata on Sturmian words, we establish some combinatorial properties of these new words. Next, the classical and palindromic complexity functions of these words are also determined. Finally, we show that these words are $2$-balanced and we establish their abelian complexity function.