Spectrum of Levy constants for quadratic irrationalities

It is proved that $\pi^2/12\log2$ is a condensation point of the set of Levy constants for quadratic irrationalities of the form $\sqrt d$. Conditions are obtained under which the Levy constant for $\sqrt d$ is separated from the left bounding point for the Levy constants, i.e., from $\log(1 + \sqrt5)/2$.