  We consider minimal resolutions of the singularities for weighted projective
planes of type $\mathbb{P}(e^2, f^2, g^2)$, where $e, f, g$ satisfy the Markoff
equation $ e^2 + f^2 + g^2 = 3efg$. We give a complete classification of such
resolutions in terms of continued fractions similar to classical work of
Frobenius. In particular, we investigate the behaviour of resolutions under
mutations and describe a Cantor set emerging as limits of continued fractions.
