2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/170609The 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.6 pages, 1 figure; revised and improved versionDynamical SystemsMathematical Physics37B10, 42A82, 52C23text