  The initial non-repetitive complexity function of an infinite word x (first
defined by Moothathu) is the function of n that counts the number of distinct
factors of length n that appear at the beginning of x prior to the first
repetition of a length-n factor. We examine general properties of the initial
non-repetitive complexity function, as well as obtain formulas for the initial
non-repetitive complexity of the Thue-Morse word, the Fibonacci word and the
Tribonacci word.
