English

Box dimension of fractal functions on attractors

Dynamical Systems 2024-10-07 v1 Metric Geometry

Abstract

We study a wide class of fractal interpolation functions in a single platform by considering the domains of these functions as general attractors. We obtain lower and upper bounds of the box dimension of these functions in a more general setup where the interpolation points need not be equally spaced, the scale vectors can be variables and the maps in the corresponding IFS can be non-affine. In particular, we obtain the exact value of the box dimension of non-affine fractal functions on general m-dimensional cubes and Sierpinski Gasket.

Keywords

Cite

@article{arxiv.2410.03144,
  title  = {Box dimension of fractal functions on attractors},
  author = {R. Pasupathi},
  journal= {arXiv preprint arXiv:2410.03144},
  year   = {2024}
}