Box dimension of generalized affine fractal interpolation functions (II)

Abstract

Let $f$ be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we estimate ${\dim }_B\Gamma f$, the box dimension of the graph of $f$, under the assumption that vertical scaling functions are of bounded variation. The main tool we use is vertical scaling matrices introduced in our previous work from 2023. We conduct a much deeper analysis of the properties of these matrices compared to our previous work. We prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the irreducibility of lower vertical scaling matrices under weaker conditions than that in our previous work.