  We generalize the construction of Roy's Fibonacci type numbers to the case of
a Sturmian recurrence and we determine the classical exponents of approximation
$\omega_2(\xi)$, $\widehat{\omega}_2(\xi)$, $\lambda_2(\xi)$,
$\widehat{\lambda}_2(\xi)$ associated with these real numbers. This also
extends similar results established by Bugeaud and Laurent in the case of
Sturmian continued fractions. More generally we provide an almost complete
description of the combined graph of parametric successive minima functions
defined by Schmidt and Summerer in dimension two for such Sturmian type
numbers. As a side result we obtain new information on the joint spectra of the
above exponents as well as a new family of numbers for which it is possible to
construct the sequence of the best rational approximations.
