We introduce computational strategies for measuring the ``size'' of the spectrum of bounded self-adjoint operators using various metrics such as the Lebesgue measure, fractal dimensions, the number of connected components (or gaps), and other spectral characteristics. Our motivation comes from the study of almost-periodic operators, particularly those that arise as models of quasicrystals. Such operators are known for intricate hierarchical patterns and often display delicate spectral properties, such as Cantor sp…