On fractal properties of Weierstrass-type functions
2019 ◽
Vol 12
(2)
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Keyword(s):
In the sequel, starting from the classical Weierstrass function defined, for any real number $x$, by $ {\mathcal W}(x)=\displaystyle \sum_{n=0}^{+\infty} \lambda^n\,\cos \left(2\, \pi\,N_b^n\,x \right)$, where $\lambda$ and $N_b$ are two real numbers such that~\mbox{$0 <\lambda<1$},~\mbox{$ N_b\,\in\,\N$} and $ \lambda\,N_b > 1 $, we highlight intrinsic properties of curious maps which happen to constitute a new class of iterated function system. Those properties are all the more interesting, in so far as they can be directly linked to the computation of the box dimension of the curve, and to the proof of the non-differentiabilty of Weierstrass type functions.
Keyword(s):
2018 ◽
Vol 11
(2)
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Keyword(s):
2006 ◽
Vol 51
(11)
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pp. 1727-1740
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2008 ◽
Vol 392-394
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pp. 575-579
2011 ◽
Vol 222
(3)
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pp. 503-513
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Keyword(s):
2014 ◽
Vol 403
◽
pp. 21-28
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Keyword(s):