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Journal Articles Proceedings of the International Geometry Center Year : 2019

On fractal properties of Weierstrass-type functions

Claire David
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Abstract

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.
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Dates and versions

hal-03698959 , version 1 (17-06-2023)

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Claire David. On fractal properties of Weierstrass-type functions. Proceedings of the International Geometry Center, 2019, 12 (2), ⟨10.15673/tmgc.v12i2.1485⟩. ⟨hal-03698959⟩
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