AUTOMATIC MAPS ON A SEMIRING WITH DIGITS
Jean‐Paul Allouche, Emmanuel Cateland, Heinz‐Otto Peitgen, Г. Скордев, Jeffrey O. Shallit · Fractals · 1995
A general framework for substitutions and automaticity of maps from a ring (or even from a semiring) with radix representation to a finite set is given. Our definition contains the classical notion of automaticity as well as the case of multidimensional automatic sequences and the case of sequences indexed by rational integers, by Gaussian integers or by quadratic irrationals.