Box dimension of the graphs of recurrent fractal interpolation functions
Abstract
Abstract Let f be a generalized affine recurrent fractal interpolation function with vertical scaling functions. In this paper, by introducing underlying local iterated function systems of f , we define restricted vertical scaling matrices. Then we analyze the irreducibility and monotonicity of spectral radii of these matrices. With these matrices, we study the oscillation sums of f . As a result, we estimate the box dimension of the graph of f by the limits of spectral radii of these matrices. In particular, we obtain an explicit formula of the box dimension of the graph of f under certain constraint conditions.
Fields of Study & Subjects
Mathematical Dynamics and Fractals
Topological and Geometric Data Analysis
Advanced Mathematical Theories and Applications
Publication details
- Journal / source
- Nonlinearity
- Volume
- 39
- Issue
- 9
- Pages
- 095013–095013
- Publication date
- 9 September 2026
- Language
- EN