Box dimension of generalized affine fractal interpolation functions

Abstract

Let $f$ be a generalized affine fractal interpolation function with a 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 Lipschitz function. By introducing vertical scaling matrices, we estimate the upper and the lower bounds of oscillations of $f$. As a result, we obtain an explicit formula of ${\dim }_B\Gamma f$ under certain constraint conditions.