DOI: 10.15673/tmgc.v11i2.1028 (eng)
Authors:
- Claire David
Abstract | Full Text: 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.
Keywords:
- Classical Weierstrass function
- box dimension