Following Inoue et al., we define a word to be a repetition if it is a
(fractional) power of exponent at least 2. A word has a repetition
factorization if it is the product of repetitions. We study repetition
factorizations in several (generalized) automatic sequences, including the
infinite Fibonacci word, the Thue-Morse word, paperfolding words, and the
Rudin-Shapiro sequence