Newman's phenomenon for generalized Thue-Morse sequences

When Thue-morse Meets Koch

In this paper, we reveal a remarkable connection between the Thue-Morse sequence and the Koch snowflake. Using turtle geometry and polygon maps, we realize the Thue-Morse sequence as the limit of polygonal curves in the plane. We then prove that a sequence of such curves converges to the Koch snowflake in the Hausdorff metric. In the final section we consider generalized Thue-Morse sequences an...

On the real roots of generalized Thue-Morse polynomials

In this article we investigate real roots of real polynomials. By results of M. Kac 8, 9, 10] we know that a polynomial of degree n has in average 2 log n real zeros. See also results of Edelman and Kostlan 5] on the same subject. Some 10 years later Erdds and OOord 7] proved that the mean number of real roots of a random polynomial of degree n with coeecients 1 is again 2 log n: This leads us ...

Fractal Sequences , Part 1 : Overview

Infinity is where things happen that don't. — S. Knight Ever since Benoit Mandelbrot published his book on fractals [1], we've become accustomed to seeing fantastic and beautiful fractal images such as the ones at the bottom of the pages of this article. A fractal is a mathematical object that exhibits self similarity — it looks the same at any scale. If you zoom in on an image of a fractal, yo...

On the Nomality of Subsequences of Generalized Thue-Morse Sequences

Doppler Tolerance, Complementary Code Sets and Generalized Thue-Morse Sequences

We generalize the construction of Doppler-tolerant Golay complementary waveforms by Pezeshki-CalderbankMoran-Howard to complementary code sets having more than two codes. This is accomplished by exploiting numbertheoretic results involving the sum-of-digits function, equal sums of like powers, and a generalization to more than two symbols of the classical two-symbol Prouhet-Thue-Morse sequence.