  We study the graph of the function $d(t)$ encoding the Hausdorff dimensions
of the classical Lagrange and Markov spectra with half-infinite lines of the
form $(-\infty, t)$. For this sake, we use the fact that the Hausdorff
dimension of dynamically Cantor sets drop after erasing an element of its
Markov partition to determine twelve nontrivial plateaux of $d(t)$. Next, we
employ rigorous numerical methods (from our recent joint paper with Pollicott)
to produce approximations of the graph of $d(t)$ between these twelve plateaux.
As a corollary, we prove that the largest ten non-trivial plateaux of $d(t)$
are exactly those plateaux with lengths $> 0.005$.
