abstract: I will discuss an approach for computing the Hausdorff dimension of an intersection of the classical Lagrange and Markov spectra with half-infinite ray d(t) = dim(M \cap (−∞,t)), that allows to plot a graph of the function d(t) with high accuracy. The talk is based on a recent joint work with Carlos Gustavo Moreira and Carlos Matheus Santos (arxiv:2212.11371).