Box dimension of generalized affine fractal interpolation functions (II)

2023/08/15 by Lai Jiang, Jiang, Lai, Huo-Jun Ruan +1 · 1 citation
Mathematics · Computer Science · Physics and Astronomy · #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #Advanced Mathematical Theories and Applications

paper · pdf · doi:10.48550/arxiv.2308.07786

Abstract

Let f be a generalized affine fractal interpolation function with vertical scaling functions. In this paper, we prove the monotonicity of spectral radii of vertical scaling matrices without additional assumptions. We also obtain the irreducibility of these matrices under certain conditions. By these results, we estimate dim_B Γf, the box dimension of the graph of f, by the limits of spectral radii of vertical scaling matrices. We also estimate dim_B Γf directly by the sum function of vertical scaling functions. As an application, we study the box dimension of the graph of a generalized Weierstrass-type function.

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• Box dimension of the graphs of recurrent fractal interpolation functions

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