Spectrum of a Rudin-Shapiro-like sequence (Q2356766)

The Rudin-Shapiro sequence is one of the few substitution sequences with an absolutely continuous spectral component. Recently, several sequences with seemingly similar properties have been proposed. For one of them, which is due to \textit{P. Lafrance} et al. [Adv. Appl. Math. 63, 19--40 (2015; Zbl 1302.68227)], the authors employ Bartlett's algorithmic approach to identify the ergodic spectral measures, which are all singular. They then argue that the diffraction measure in the balanced weight case is purely singular continuous.