The singular continuous diffraction measure of the Thue-Morse chain
  The paradigm for singular continuous spectra in symbolic dynamics and in mathematical diffraction is provided by the Thue-Morse chain, in its realisation as a binary sequence with values in $\{\pm 1\}$. We revisit this example and derive a functional equation together with an explicit form of the corresponding singular continuous diffraction measure, which is related to the known representation as a Riesz product. 
Michael Baake (Bielefeld), Uwe Grimm (Milton Keynes)