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A relative of the Thue-Morse sequence

✍ Scribed by Jean-Paul Allouche; André Arnold; Jean Berstel; Srećko Brlek; William Jockusch; Simon Plouffe; Bruce E. Sagan

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
240 KB
Volume
139
Category
Article
ISSN
0012-365X

No coin nor oath required. For personal study only.

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Fractal Behaviour of Diffraction Pattern
Fractal Behaviour of Diffraction Pattern of Thue–Morse Sequence
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The Thue-Morse sequence is an example of an aperiodic structure with a singular continuous contribution to the diffraction pattern. Many satellites observed near the main diffraction peaks have been indexed and their intensities have been numerically calculated. Details of such a calculation are pre

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Given two words u and v, the binomial coefficient (t) is the number of ways v appears as a subword (or subsequence) of u. The Thue-Morse sequence is the infinite word t = abbabaab . . . obtained by iteration of the morphism r(a) = ab and z(b) = ba. We show that, for every prime p, and every positive

On Finite Pseudorandom Binary Sequences:
On Finite Pseudorandom Binary Sequences: II. The Champernowne, Rudin–Shapiro, and Thue–Morse Sequences, A Further Construction
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Special finite binary sequences are tested for pseudorandomness. As measures of pseudorandomness, well-distribution relative to arithmetic progressions and small (auto)correlation are used. These properties of the Champernowne, Thue Morse, and Rudin Shapiro sequences are studied and it is shown that