Correlation and spectral properties of higher-dimensional paperfolding and Rudin–Shapiro sequences
Anna Greta Barbe, Fritz V. Haeseler · Journal of Physics A Mathematical and General · 2005
We consider higher-dimensional generalizations of the classical one-dimensional 2-automatic paperfolding and Rudin–Shapiro sequences on . This is done by considering the same automaton-structure as in the one-dimensional case, but using binary number systems in instead of in . The correlation function and the diffraction spectrum for the resulting m -dimensional paperfolding and Rudin–Shapiro point sets are calculated through the corresponding sequences with values ±1. They are shown to be quasi-independent of the dimension m and of the particular binary number system under consideration. It is shown that any paperfolding sequence thus obtained has a discrete spectrum. The Rudin–Shapiro sequences have an absolutely continuous Lebesgue spectral measure.