  We take a global view at substitution invariant Sturmian sequences. We show
that homogeneous substitution invariant Sturmian sequences $s_{\alpha,\alpha}$
can be indexed by two binary trees, associated directly to Johannes Kepler's
tree of harmonic fractions from 1619. We obtain similar results for the
inhomogeneous sequences $s_{\alpha,1-\alpha}$ and $s_{\alpha,0}$.
