Box dimension of generalized affine fractal interpolation functions

Abstract

Let $f$ be a generalized affine fractal interpolation function with vertical scaling function $S$. In this paper, we study ${\dim }_B\Gamma f$, the box dimension of the graph of $f$, under the assumption that $S$ is a Lipschtz function. By introducing vertical scaling matrices, we estimate the upper bound and the lower bound of oscillations of $f$. As a result, we obtain explicit formula of ${\dim }_B\Gamma f$ under certain constraint conditions.

18 pages, 1 figure