%0 Journal Article
%T Fractal Curves from Prime Trigonometric Series
%A Dimitris Vartziotis
%A Doris Bohnet
%J -
%D 2018
%R https://doi.org/10.3390/fractalfract2010002
%X Abstract We study the convergence of the parameter family of series: V ¦Á , ¦Â ( t ) = ¡Æ p p £¿ ¦Á exp ( 2 ¦Ð i p ¦Â t ) , ¦Á , ¦Â ¡Ê R > 0 , t ¡Ê [ 0 , 1 ) defined over prime numbers p and, subsequently, their differentiability properties. The visible fractal nature of the graphs as a function of ¦Á , ¦Â is analyzed in terms of H£¿lder 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. View Full-Tex
%K trigonometric series
%K lacunary series
%K H£¿lder continuity
%K fractality
%K random Fourier series
%K prime distribution
%U https://www.mdpi.com/2504-3110/2/1/2