Lagrange spectrum in diophantine approximation theory

You can find graphical visualizations of Lagrange spectrum in this recent paper:

"Approximation of the Lagrange and Markov spectra" Vincent Delecroix, Carlos Matheus, Carlos Gustavo Moreira https://arxiv.org/abs/1908.03773

There is also a picture of the Lagrange spectrum until sqrt(12) in the cover of the following book: https://worldscientific.com/worldscibooks/10.1142/11965