Proceedings of the International Geometry Center

ISSN-print: 2072-9812
ISSN-online: 2409-8906
ISO: 26324:2012

Bypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function


Claire David


In the following, bypassing dynamical systems tools, we propose a simple means of computing the box dimension of the graph of the classical Weierstrass function defined, for any real number~$x$, by
\[{\mathcal W}(x)= \sum_{n=0}^{+\infty} \lambda^n\,\cos \left ( 2\, \pi\,N_b^n\,x \right),\]

where $\lambda$ and $N_b$ are two real numbers such that $0 <\lambda<1$, $N_b\,\in\,\N$ and $\lambda\,N_b >1$, using a sequence a graphs that approximate the studied one.

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Як цитувати
David, C. (2018). Bypassing dynamical systems: a simple way to get the box-counting dimension of the graph of the Weierstrass function. Proceedings of the International Geometry Center, 11(2).


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