Three types of the Parikh mapping are introduced, namely, alphabetic, alphabetic-basis and basis. Explicit expressions for attractors of the k-th order in bases n >= 8, including countable ones, are found. Properties for the alphabetic, alphabetic-basis and basis Parikh vectors are given at each step of the Parikh mapping. The maximum number of iterations leading to attractors of the k-th order in the basis n is determined.

翻译：引入三种类型的Parikh映射，即字母型、字母-基型与基型。本文给出了在基n≥8中（包括可数吸引子）k阶吸引子的显式表达式，描述了Parikh映射每步迭代中字母型、字母-基型与基型Parikh向量的性质，并确定了基n中达到k阶吸引子所需的最大迭代次数。