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arXiv · 2208.04126

Box dimension of generalized affine fractal interpolation functions

Lai Jiang·Huo-Jun Ruan
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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.

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Lai Jiang, Huo-Jun Ruan. 2022-08-08. Box dimension of generalized affine fractal interpolation functions. https://arxiv.org/abs/2208.04126

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