Fractal Curves from Prime Trigonometric Series
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TWT GmbH Science & Innovation, Mathematical Research, Ernsthaldenstr. 17, 70565 Stuttgart, Germany
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Received: 10 November 2017 / Revised: 26 December 2017 / Accepted: 26 December 2017 / Published: 3 January 2018
We study the convergence of the parameter family of series:
defined over prime numbers p
and, subsequently, their differentiability properties. The visible fractal nature of the graphs as a function of
is analyzed in terms of Hölder continuity, self-similarity and fractal dimension, backed with numerical results. Although this series is not a lacunary series, it has properties in common, such that we also discuss the link of this series with random walks and, consequently, explore its random properties numerically.
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MDPI and ACS Style
Vartziotis, D.; Bohnet, D. Fractal Curves from Prime Trigonometric Series. Fractal Fract 2018, 2, 2.
Vartziotis D, Bohnet D. Fractal Curves from Prime Trigonometric Series. Fractal and Fractional. 2018; 2(1):2.
Vartziotis, Dimitris; Bohnet, Doris. 2018. "Fractal Curves from Prime Trigonometric Series." Fractal Fract 2, no. 1: 2.
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