  We show that the size $\gamma(t_n)$ of the smallest string attractor of the
$n$th Thue-Morse word $t_n$ is 4 for any $n\geq 4$, disproving the conjecture
by Mantaci et al. [ICTCS 2019] that it is $n$. We also show that $\delta(t_n) =
\frac{10}{3+2^{4-n}}$ for $n \geq 3$, where $\delta(w)$ is the maximum over all
$k = 1,\ldots,|w|$, the number of distinct substrings of length $k$ in $w$
divided by $k$, which is a measure of repetitiveness recently studied by
Kociumaka et al. [LATIN 2020]. Furthermore, we show that the number $z(t_n)$ of
factors in the self-referencing Lempel-Ziv factorization of $t_n$ is exactly
$2n$.
