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}
}