  For any infinite word $w$ on a finite alphabet $A$, the complexity function
$p_w$ of $w$ is the sequence counting, for each non-negative $n$, the number
$p_w(n)$ of words of length $n$ on the alphabet $A$ that are factors of the
infinite word $w$ and the the entropy of $w$ is the quantity
$E(w)=\lim\limits_{n\to\infty}\frac 1n\log p_w(n)$. For any given function $f$
with exponential growth, Mauduit and Moreira introduced in [MM17] the notion of
word entropy $E_W(f) = \sup \{E(w), w \in A^{{\mathbb N}}, p_w \le f \}$ and
showed its links with fractal dimensions of sets of infinite sequences with
complexity function bounded by $f$. The goal of this work is to give an
algorithm to estimate with arbitrary precision $E_W(f)$ from finitely many
values of $f$.
