Abstract
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.
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