English

On an abrasion motivated fractal model

Dynamical Systems 2024-09-12 v2

Abstract

In this paper, we consider a fractal model motivated by the abrasion of convex polyhedra, where the abrasion is realised by chipping small neighbourhoods of vertices. After providing a formal description of the successive chippings, we show that the net of edges converge to a compact limit set under mild assumptions. Furthermore, we study the upper box-counting dimension and the Hausdorff dimension of the limiting object of the net of edges after infinitely many chipping.

Keywords

Cite

@article{arxiv.2402.17765,
  title  = {On an abrasion motivated fractal model},
  author = {Balázs Bárány and Gábor Domokos and Ágoston Szesztay},
  journal= {arXiv preprint arXiv:2402.17765},
  year   = {2024}
}