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Box dimension of generalized affine fractal interpolation functions
- Publication Year :
- 2022
-
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.<br />Comment: 18 pages, 1 figure
- Subjects :
- Mathematics - Metric Geometry
Primary 28A80, Secondary 41A30
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2208.04126
- Document Type :
- Working Paper