The Bourgain spherical harmonics formed from Rudin-Shapiro sequences equidistribute on S^3, while their semiclassical measure is a singular measure supported on Clifford tori.
Bourgain, On uniformly bounded bases in spaces of holomorphic functions
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Semiclassical measure of the spherical harmonics by Bourgain on $\mathbb{S}^3$
The Bourgain spherical harmonics formed from Rudin-Shapiro sequences equidistribute on S^3, while their semiclassical measure is a singular measure supported on Clifford tori.