Fractal Curves from Prime Trigonometric Series
NIKI Ltd. Digital Engineering, Research Center, 205 Ethnikis Antistasis Street, 45500 Katsika, Ioannina, Greece
TWT GmbH Science & Innovation, Mathematical Research, Ernsthaldenstr. 17, 70565 Stuttgart, Germany
Author to whom correspondence should be addressed.
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.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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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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